| Year | Award | Nominated work | Result |
|---|
| 1983 | New York Film Critics Circle Award for Best Supporting Actor | The Right Stuff | Nominated |
| 1984 | Obie Award for Distinguished Performance by an Actor | Fool for Love | Won |
| 1986 | Drama Desk Award for Outstanding Actor in a Play | Precious Sons | Won |
| Theatre World Award | Won |
| 1989 | Saturn Award for Best Actor | The Abyss | Nominated |
| 1992 | Valladolid International Film Festival Award for Best Actor | Glengarry Glen Ross | Won |
| 1995 | Critics' Choice Movie Award for Best Supporting Actor | Nixon , Apollo 13 , and Just Cause | Won |
| Southeastern Film Critics Association Award for Best Supporting Actor | Apollo 13 | Won |
| Dallas-Fort Worth Film Critics Association Award for Best Supporting Actor | Runner-up |
| Chicago Film Critics Association Award for Best Supporting Actor | Nominated |
| Lucille Lortel Award for Outstanding Lead Actor in a Play | Simpatico | Won |
| 1996 | Bronze Wrangler for Television Feature Film | Riders of the Purple Sage | Won |
| 1998 | Blockbuster Entertainment Award for Favorite Supporting Actor — Drama | The Truman Show | Won |
| National Board of Review Award for Best Supporting Actor | Won |
| Southeastern Film Critics Association Award for Best Supporting Actor | Won |
| Online Film Critics Society Award for Best Supporting Actor | Nominated |
| Saturn Award for Best Supporting Actor | Nominated |
| 2000 | Toronto Film Critics Association Award for Best Actor | Pollock | Won |
| Satellite Award for Best Actor – Motion Picture Drama | Nominated |
| 2001 | Satellite Award for Best Supporting Actor – Motion Picture | A Beautiful Mind | Nominated |
| 2002 | Critics' Choice Movie Award for Best Acting Ensemble | The Hours | Nominated |
| Dallas-Fort Worth Film Critics Association Award for Best Supporting Actor | 3rd Place |
| London Film Critics Circle Award for Actor of the Year | Nominated |
| Phoenix Film Critics Society Award for Best Cast | Nominated |
| Italian Online Movie Award for Best Cast | Won |
| Italian Online Movie Award for Best Supporting Actor | Won |
| 2005 | Satellite Award for Best Actor – Miniseries or Television Film | Empire Falls | Nominated |
| Women's Image Network Award for Best Actor in a Made-for-TV Movie/Miniseries | Won |
| National Society of Film Critics Award for Best Supporting Actor | A History of Violence | Won |
| 2007 | Drama Desk Award for Outstanding Solo Performance | Wrecks | Nominated |
| Outer Critics Circle Award for Outstanding Solo Performance | Nominated |
| 2008 | Boston Film Festival Prize for Best Screenplay Adaptation | Appaloosa | Won |
| Bronze Wrangler for Theatrical Motion Picture | Won |
| Critics' Choice Movie Award for Best Acting Ensemble | Gone Baby Gone | Nominated |
| 2012 | Golden Nymph Award for Best Performance by an Actor – Television Film | Game Change | Nominated |
| 2014 | Women Film Critics Circle - Adrienne Shelly Award | Frontera | Won |
| 2016 | Lucille Lortel Award for Outstanding Lead Actor in a Play | Buried Child | Nominated |
| 2017 | Saturn Award for Best Supporting Actor on Television | Westworld | Won |
| 2019 | Saturn Award for Best Supporting Actor on Television | Nominated |