- In 2000, received Academy Award for Best Actor in a Leading Role
- In 2000, received BAFTA Award for Best Actor
- In 2000, received London Critics Circle Film Award for Actor of the Year
- In 2000, received Chicago Film Critics Association Award for Best Actor
- In 2000, received Screen Actors Guild Award for Outstanding Performance by a Cast in a Motion Picture
- In 2000, received Screen Actors Guild Award for Outstanding Performance by a Male Actor in a Leading Role
- In 2000, received Sundance Film Festival Award for Tribute to Independent Vision
- In 1999, received London Critics Circle Award for Best Actor
- In 1999, received Olivier Award for Best Actor in a Play
- In 1999, received Toronto Film Critics Association Award for Best Actor
- In 1999, received Outer Critics Circle Award for Outstanding Actor in a Play
- In 1998, received Evening Standard Award for Best Actor
- In 1997, received Boston Society of Film Critics Award for Best Supporting Actor
- In 1996, received Broadcast Film Critics Association Award for Best Supporting Actor
- In 1996, received Chicago Film Critics Association Award for Best Supporting Actor
- In 1996, received Academy Award for Best Actor in a Supporting Role
- In 1996, received MTV Movie Award for Best Villain
- In 1995, received National Board of Review Award for Best Supporting Actor
- In 1995, received Boston Society of Film Critics Award for Best Supporting Actor
- In 1995, received National Board of Review Award for Best Acting by an Ensemble
- In 1995, received New York Film Critics Circle Award for Best Supporting Actor
- In 1991, received Drama Desk Award for Outstanding Featured Actor in a Play
- In 1991, received Tony Award for Featured Actor in a Play
