content: <PAGE>   1
                                                             Registration No. 333-
  
       As filed with the Securities and Exchange Commission on June 11, 1999
  ================================================================================
  
  
                         SECURITIES AND EXCHANGE COMMISSION
                               Washington, D.C. 20549
  
                                      --------
  
                                      FORM S-8
                               REGISTRATION STATEMENT
                                        UNDER
                             THE SECURITIES ACT OF 1933
  
                                      --------
  
                             NOBLE DRILLING CORPORATION
               (Exact name of registrant as specified in its charter)
  
           DELAWARE                                        73-0374541
  (State or other jurisdiction                (I.R.S. Employer Identification No.)
  of incorporation or organization)
  
  
     10370 RICHMOND AVENUE, SUITE 400
             HOUSTON, TEXAS                                    77042
  (Address of Principal Executive Offices)                   (Zip Code)
  
  
                                      --------
  
                    NOBLE DRILLING CORPORATION 1991 STOCK OPTION
                              AND RESTRICTED STOCK PLAN
                              (Full title of the plan)
  
                                      --------
  
          ROBERT D. CAMPBELL                                      COPY TO:
               PRESIDENT                                       DAVID L. EMMONS
       NOBLE DRILLING CORPORATION                          THOMPSON & KNIGHT, P.C.
     10370 RICHMOND AVENUE, SUITE 400                        1700 PACIFIC AVENUE
          HOUSTON, TEXAS 77042                                   SUITE 3300
  (Name and address of agent for service)                    DALLAS, TEXAS 75201
  
  
                                   (713) 974-3131
                            (Telephone number, including
                          area code, of agent for service)
  
  
  <TABLE>
  <CAPTION>
                           CALCULATION OF REGISTRATION FEE
  --------------------------------------------------------------------------------
     Title of                        Proposed     Proposed Maximum       Amount
    Securities        Amount         Maximum          Aggregate            of
       to be           to be      Offering Price      Offering        Registration
    Registered     Registered(1)   per Share(2)       Price(2)            Fee
  --------------------------------------------------------------------------------
  <S>              <C>            <C>             <C>                 <C>
   Common Stock,     5,000,000
  par value $.10      shares          $18.375      $91,875,000.00      $25,541.25
     per share
  --------------------------------------------------------------------------------
  </TABLE>
  
  (1)  Pursuant to Rule 416 under the Securities Act of 1933, shares issuable upon
       any stock split, stock dividend or similar transaction with respect to
       these shares are also being registered hereunder.
  
  (2)  Estimated solely for the purpose of determining the registration fee
       pursuant to Rule 457(h) on the basis of the average of the high and low
       sales prices of the Common Stock reported on the New York Stock Exchange
       Composite Tape on June 4, 1999.
  
  
  ================================================================================
  
  <PAGE>   2
  
  
                                       PART I
  
                         INCORPORATION OF CONTENTS OF PRIOR
                               REGISTRATION STATEMENTS
  
        The contents of Registration Statement No. 33-46724 relating to the Noble
  Drilling Corporation 1991 Stock Option and Restricted Stock Plan (the "Plan")
  filed by the Registrant with the Securities and Exchange Commission (the
  "Commission") on April 1, 1992, Registration Statement No. 33-57675 relating to
  the Plan filed by the Registrant with the Commission on February 13, 1995, and
  Registration Statement No. 333-25857 relating to the Plan filed by the
  Registrant with the Commission on April 25, 1997 (together, the "Prior
  Registration Statements") are incorporated herein by reference pursuant to
  General Instruction E to Form S-8. The purpose of this Registration Statement is
  to register 5,000,000 additional shares of Common Stock of the Registrant for
  offer and sale pursuant to the Plan.
  
                                       PART II
  
                 INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
  
  Item 6. Indemnification of Directors and Officers.
  
        The Registrant is a Delaware corporation. Under Section 145 of the General
  Corporation Law of the State of Delaware, the Registrant has the power to
  indemnify its directors and officers, subject to certain limitations.
  
        Reference is made to Article VI of the Bylaws of the Registrant, which
  provides for indemnification of directors and officers of the Registrant under
  certain circumstances.
  
        The Registrant has entered into indemnity agreements with the Registrant's
  directors and bylaw officers intended to provide for indemnification to the
  fullest extent permitted by law.
  
        Pursuant to the General Corporation Law of the State of Delaware, the
  Certificate of Incorporation of the Registrant limits the personal liability of
  the directors of the Registrant to the Registrant or its stockholders for
  monetary damages for breach of fiduciary duty under certain circumstances.
  
        The Registrant also maintains insurance to protect itself and its
  directors, officers, employees and agents against expenses, liabilities and
  losses incurred by such persons in connection with their service in the
  foregoing capacities.
  
        The foregoing summaries are necessarily subject to the complete text of
  the statute, bylaw, agreement, certificate of incorporation and insurance policy
  referred to above and are qualified in their entirety by reference thereto.
  
  Item 8. Exhibits.
  
        In addition to the exhibits filed with or incorporated by reference in the
  Prior Registration Statements, the following documents are filed or incorporated
  by reference as exhibits to this Registration Statement:
  
  <TABLE>
  <CAPTION>
  Exhibit Number          Description
  --------------          -----------
  <S>                     <C>
  4.1                     Noble Drilling Corporation 1991 Stock Option and
                          Restricted Stock Plan, as amended effective as of
                          February 4, 1999.
  
  5.1                     Opinion of Thompson & Knight, A Professional Corporation.
  
  23.1                    Consent of Thompson & Knight, A Professional Corporation
                          (contained in its opinion filed herewith as Exhibit
                          5.1).
  
  23.2                    Consent of PricewaterhouseCoopers LLP.
  
  24.1                    Power of Attorney (included on the signature page of
                          this Registration Statement).
  </TABLE>
  
  
  
                                         1
  <PAGE>   3
  
                                     SIGNATURES
  
        Pursuant to the requirements of the Securities Act of 1933, the Registrant
  certifies that it has reasonable grounds to believe that it meets all of the
  requirements for filing on Form S-8 and has duly caused this Registration
  Statement to be signed on its behalf by the undersigned, thereunto duly
  authorized, in Houston, Texas on the 10th day of June 1999.
  
                                          NOBLE DRILLING CORPORATION
                                          (Registrant)
  
                                          By:   /s/ ROBERT D. CAMPBELL
                                                ----------------------------------
                                                Robert D. Campbell, President
  
        Pursuant to the requirements of the Securities Act of 1933, this
  Registration Statement has been signed by the following persons in the
  capacities and on the date indicated.
  
        Each person whose signature appears below constitutes and appoints James
  C. Day and Robert D. Campbell, and each of them (with full power to each of them
  to act alone), his true and lawful attorney-in-fact and agent, with full power
  of substitution and resubstitution, for him and in his name, place and stead, in
  any and all capacities to sign on his behalf individually and in each capacity
  stated below any amendment, including post-effective amendments, to this
  Registration Statement and any Registration Statement (including any amendment
  thereto) for this offering that is to be effective upon filing pursuant to Rule
  462(b) under the Securities Act of 1933, as amended, and to file the same, with
  all exhibits thereto and other documents in connection therewith, with the
  Securities and Exchange Commission, granting unto said attorneys-in-fact and
  agents, and each of them, full power and authority to do and perform each and
  every act and thing requisite and necessary to be done in and about the
  premises, as fully to all intents and purposes as he might or could do in
  person, hereby ratifying and confirming all that said attorneys-in-fact and
  agents and either of them, or their substitutes, may lawfully do or cause to be
  done by virtue hereof.
  
  <TABLE>
  <CAPTION>
  Signature                           Title                                            Date
  ---------                           -----                                            ----
  <S>                                 <C>                                              <C>
  /s/ JAMES C. DAY                    Chairman and Chief Executive                     June 10, 1999
  -----------------------------       Officer and Director
  James C. Day                        (Principal Executive Officer)
  
  /s/ BYRON L. WELLIVER               Senior Vice President - Finance,                 June 10, 1999
  -----------------------------       Treasurer and Controller
  Byron L. Welliver                   (Principal Financial and Accounting Officer)
  
  /s/ ROBERT D. CAMPBELL              President and Director                           June 10, 1999
  -----------------------------
  Robert D. Campbell
  
  /s/ MICHAEL A. CAWLEY               Director                                         June 10, 1999
  -----------------------------
  Michael A. Cawley
  
  /s/ LAWRENCE J. CHAZEN              Director                                         June 10, 1999
  -----------------------------
  Lawrence J. Chazen
  
  /s/ TOMMY C. CRAIGHEAD              Director                                         June 10, 1999
  -----------------------------
  Tommy C. Craighead
  
  /s/ WILLIAM J. DORE                 Director                                         June 10, 1999
  -----------------------------
  William J. Dore
  
  /s/ JAMES L. FISHEL                 Director                                         June 10, 1999
  -----------------------------
  James L. Fishel
  
  /s/ MARC E. LELAND                  Director                                         June 10, 1999
  -----------------------------
  Marc E. Leland
  
  
  -----------------------------       Director
  William A. Sears
  </TABLE>
  
  
                                         2
  <PAGE>   4
  
                                  INDEX TO EXHIBITS
  
  
  <TABLE>
  <CAPTION>
  Exhibit Number          Description
  --------------          -----------
  <S>                     <C>
  4.1                     Noble Drilling Corporation 1991 Stock Option and
                          Restricted Stock Plan, as amended effective as of
                          February 4, 1999.
  
  5.1                     Opinion of Thompson & Knight, A Professional Corporation.
  
  23.1                    Consent of Thompson & Knight, A Professional Corporation
                          (contained in its opinion filed herewith as Exhibit
                          5.1).
  
  23.2                    Consent of PricewaterhouseCoopers LLP.
  
  24.1                    Power of Attorney (included on the signature page of
                          this Registration Statement).
  </TABLE>
metadata_documents: [{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 11971}]
metadata_filer: {"company-data": {"conformed-name": "NOBLE DRILLING CORP", "cik": "0000777201", "assigned-sic": "1381", "irs-number": "730374541", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-80511", "film-number": "99645031"}, "business-address": {"street1": "10370 RICHMOND AVE STE 400", "city": "HOUSTON", "state": "TX", "zip": "77042", "phone": "7139743131"}, "mail-address": {"street1": "10370 RICHMOND AVE", "street2": "STE 400", "city": "HOUSTON", "state": "TX", "zip": "77042"}}
text: 1
                                                             Registration No. 333-
  
       As filed with the Securities and Exchange Commission on June 11, 1999
  ================================================================================
  
                         SECURITIES AND EXCHANGE COMMISSION
                               Washington, D.C. 20549
  
                                      --------
  
                                      FORM S-8
                               REGISTRATION STATEMENT
                                        UNDER
                             THE SECURITIES ACT OF 1933
  
                                      --------
  
                             NOBLE DRILLING CORPORATION
               (Exact name of registrant as specified in its charter)
  
           DELAWARE                                        73-0374541
  (State or other jurisdiction                (I.R.S. Employer Identification No.)
  of incorporation or organization)
  
     10370 RICHMOND AVENUE, SUITE 400
             HOUSTON, TEXAS                                    77042
  (Address of Principal Executive Offices)                   (Zip Code)
  
                                      --------
  
                    NOBLE DRILLING CORPORATION 1991 STOCK OPTION
                              AND RESTRICTED STOCK PLAN
                              (Full title of the plan)
  
                                      --------
  
          ROBERT D. CAMPBELL                                      COPY TO:
               PRESIDENT                                       DAVID L. EMMONS
       NOBLE DRILLING CORPORATION                          THOMPSON & KNIGHT, P.C.
     10370 RICHMOND AVENUE, SUITE 400                        1700 PACIFIC AVENUE
          HOUSTON, TEXAS 77042                                   SUITE 3300
  (Name and address of agent for service)                    DALLAS, TEXAS 75201
  
                                   (713) 974-3131
                            (Telephone number, including
                          area code, of agent for service)
  CALCULATION OF REGISTRATION FEE
  --------------------------------------------------------------------------------
     Title of                        Proposed     Proposed Maximum       Amount
    Securities        Amount         Maximum          Aggregate            of
       to be           to be      Offering Price      Offering        Registration
    Registered     Registered(1)   per Share(2)       Price(2)            Fee
  --------------------------------------------------------------------------------
  Common Stock,     5,000,000
  par value $.10      shares          $18.375      $91,875,000.00      $25,541.25
     per share
  --------------------------------------------------------------------------------
  (1)  Pursuant to Rule 416 under the Securities Act of 1933, shares issuable upon
       any stock split, stock dividend or similar transaction with respect to
       these shares are also being registered hereunder.
  
  (2)  Estimated solely for the purpose of determining the registration fee
       pursuant to Rule 457(h) on the basis of the average of the high and low
       sales prices of the Common Stock reported on the New York Stock Exchange
       Composite Tape on June 4, 1999.
  
  ================================================================================
  2
  
                                       PART I
  
                         INCORPORATION OF CONTENTS OF PRIOR
                               REGISTRATION STATEMENTS
  
        The contents of Registration Statement No. 33-46724 relating to the Noble
  Drilling Corporation 1991 Stock Option and Restricted Stock Plan (the "Plan")
  filed by the Registrant with the Securities and Exchange Commission (the
  "Commission") on April 1, 1992, Registration Statement No. 33-57675 relating to
  the Plan filed by the Registrant with the Commission on February 13, 1995, and
  Registration Statement No. 333-25857 relating to the Plan filed by the
  Registrant with the Commission on April 25, 1997 (together, the "Prior
  Registration Statements") are incorporated herein by reference pursuant to
  General Instruction E to Form S-8. The purpose of this Registration Statement is
  to register 5,000,000 additional shares of Common Stock of the Registrant for
  offer and sale pursuant to the Plan.
  
                                       PART II
  
                 INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
  
  Item 6. Indemnification of Directors and Officers.
  
        The Registrant is a Delaware corporation. Under Section 145 of the General
  Corporation Law of the State of Delaware, the Registrant has the power to
  indemnify its directors and officers, subject to certain limitations.
  
        Reference is made to Article VI of the Bylaws of the Registrant, which
  provides for indemnification of directors and officers of the Registrant under
  certain circumstances.
  
        The Registrant has entered into indemnity agreements with the Registrant's
  directors and bylaw officers intended to provide for indemnification to the
  fullest extent permitted by law.
  
        Pursuant to the General Corporation Law of the State of Delaware, the
  Certificate of Incorporation of the Registrant limits the personal liability of
  the directors of the Registrant to the Registrant or its stockholders for
  monetary damages for breach of fiduciary duty under certain circumstances.
  
        The Registrant also maintains insurance to protect itself and its
  directors, officers, employees and agents against expenses, liabilities and
  losses incurred by such persons in connection with their service in the
  foregoing capacities.
  
        The foregoing summaries are necessarily subject to the complete text of
  the statute, bylaw, agreement, certificate of incorporation and insurance policy
  referred to above and are qualified in their entirety by reference thereto.
  
  Item 8. Exhibits.
  
        In addition to the exhibits filed with or incorporated by reference in the
  Prior Registration Statements, the following documents are filed or incorporated
  by reference as exhibits to this Registration Statement:
  Exhibit Number          Description
  --------------          -----------
  4.1                     Noble Drilling Corporation 1991 Stock Option and
                          Restricted Stock Plan, as amended effective as of
                          February 4, 1999.
  
  5.1                     Opinion of Thompson & Knight, A Professional Corporation.
  
  23.1                    Consent of Thompson & Knight, A Professional Corporation
                          (contained in its opinion filed herewith as Exhibit
                          5.1).
  
  23.2                    Consent of PricewaterhouseCoopers LLP.
  
  24.1                    Power of Attorney (included on the signature page of
                          this Registration Statement).
  1
  3
  
                                     SIGNATURES
  
        Pursuant to the requirements of the Securities Act of 1933, the Registrant
  certifies that it has reasonable grounds to believe that it meets all of the
  requirements for filing on Form S-8 and has duly caused this Registration
  Statement to be signed on its behalf by the undersigned, thereunto duly
  authorized, in Houston, Texas on the 10th day of June 1999.
  
                                          NOBLE DRILLING CORPORATION
                                          (Registrant)
  
                                          By:   /s/ ROBERT D. CAMPBELL
                                                ----------------------------------
                                                Robert D. Campbell, President
  
        Pursuant to the requirements of the Securities Act of 1933, this
  Registration Statement has been signed by the following persons in the
  capacities and on the date indicated.
  
        Each person whose signature appears below constitutes and appoints James
  C. Day and Robert D. Campbell, and each of them (with full power to each of them
  to act alone), his true and lawful attorney-in-fact and agent, with full power
  of substitution and resubstitution, for him and in his name, place and stead, in
  any and all capacities to sign on his behalf individually and in each capacity
  stated below any amendment, including post-effective amendments, to this
  Registration Statement and any Registration Statement (including any amendment
  thereto) for this offering that is to be effective upon filing pursuant to Rule
  462(b) under the Securities Act of 1933, as amended, and to file the same, with
  all exhibits thereto and other documents in connection therewith, with the
  Securities and Exchange Commission, granting unto said attorneys-in-fact and
  agents, and each of them, full power and authority to do and perform each and
  every act and thing requisite and necessary to be done in and about the
  premises, as fully to all intents and purposes as he might or could do in
  person, hereby ratifying and confirming all that said attorneys-in-fact and
  agents and either of them, or their substitutes, may lawfully do or cause to be
  done by virtue hereof.
  Signature                           Title                                            Date
  ---------                           -----                                            ----
  /s/ JAMES C. DAY                    Chairman and Chief Executive                     June 10, 1999
  -----------------------------       Officer and Director
  James C. Day                        (Principal Executive Officer)
  
  /s/ BYRON L. WELLIVER               Senior Vice President - Finance,                 June 10, 1999
  -----------------------------       Treasurer and Controller
  Byron L. Welliver                   (Principal Financial and Accounting Officer)
  
  /s/ ROBERT D. CAMPBELL              President and Director                           June 10, 1999
  -----------------------------
  Robert D. Campbell
  
  /s/ MICHAEL A. CAWLEY               Director                                         June 10, 1999
  -----------------------------
  Michael A. Cawley
  
  /s/ LAWRENCE J. CHAZEN              Director                                         June 10, 1999
  -----------------------------
  Lawrence J. Chazen
  
  /s/ TOMMY C. CRAIGHEAD              Director                                         June 10, 1999
  -----------------------------
  Tommy C. Craighead
  
  /s/ WILLIAM J. DORE                 Director                                         June 10, 1999
  -----------------------------
  William J. Dore
  
  /s/ JAMES L. FISHEL                 Director                                         June 10, 1999
  -----------------------------
  James L. Fishel
  
  /s/ MARC E. LELAND                  Director                                         June 10, 1999
  -----------------------------
  Marc E. Leland
  
  -----------------------------       Director
  William A. Sears
  2
  4
  
                                  INDEX TO EXHIBITS
  Exhibit Number          Description
  --------------          -----------
  4.1                     Noble Drilling Corporation 1991 Stock Option and
                          Restricted Stock Plan, as amended effective as of
                          February 4, 1999.
  
  5.1                     Opinion of Thompson & Knight, A Professional Corporation.
  
  23.1                    Consent of Thompson & Knight, A Professional Corporation
                          (contained in its opinion filed herewith as Exhibit
                          5.1).
  
  23.2                    Consent of PricewaterhouseCoopers LLP.
  
  24.1                    Power of Attorney (included on the signature page of
                          this Registration Statement).