- In 2009, received Academy Award for Best Performance by an Actor in a Leading Role
- In 2009, received National Society of Film Critics Award for Best Actor
- In 2009, received Broadcast Film Critics Association Award for Best Actor
- In 2009, received Broadcast Film Critics Association Award for Best Ensemble
- In 2009, received Screen Actors Guild Award for Outstanding Performance by a Male Actor in a Leading Role
- In 2008, received New York Film Critics Circle Award for Best Actor
- In 2008, received Boston Society of Film Critics Award for Best Actor
- In 2008, received Los Angeles Film Critics Association Award for Best Actor
- In 2008, received San Francisco Film Critics Award for Best Actor
- In 2004, received Academy Award for Best Actor in a Leading Role
- In 2004, received Golden Globe Award for Best Performance by an Actor in a Motion Picture - Drama
- In 2004, received Broadcast Film Critics Association Award for Best Actor
- In 2004, received Independent Spirit Award for Special Distinction
- In 2003, received Venice Film Festival Award for Best Actor
- In 2003, received Boston Society of Film Critics Award for Best Ensemble Cast
- In 2003, received National Board of Review Award for Best Actor
- In 2002, received Venice Film Festival UNESCO Award
- In 1998, received Venice Film Festival Award for Best Actor
- In 1997, received Cannes Film Festival Award for Best Actor
- In 1996, received Independent Spirit Award for Best Male Lead
- In 1996, received Silver Berlin Bear Award for Best Actor
- In 1983, received Los Angeles Film Critics Association Award for New Generation
