| Work | Year | Association / Category | Results | Ref |
| —N/a | 1995 | Clarence Derwent Award for Best Supporting Male | Won | |
| Arcadia | Theatre World Award for Best Actor | Won | |
| The Three Sisters | 1997 | Drama Desk Award for Outstanding Featured Actor in a Play | Nominated | |
| The Hi-Lo Country | 1998 | National Board of Review Award for Breakthrough Performance – Male | Won | |
| 1999 | Western Heritage Award for Bronze Wrangler | Won | |
| Jesus's Son | 2000 | Paris Film Festival for Best Actor | Won | |
| Almost Famous | 2001 | Blockbuster Entertainment Award for Favorite Actor – Drama / Romance | Nominated | |
| MTV Movie + TV Award for Best Line from a Movie ("I am a Golden God!") | Nominated | |
| Online Film Critics Society Award for Best Ensemble | Won | |
| Screen Actors Guild Award for Outstanding Performance by a Cast in a Motion Picture | Nominated | |
| Jesus's SonAlmost Famous | Vancouver Film Critics Circle Award for Best Actor | Nominated | |
| Jesus's Son | Independent Spirit Award for Best Male Lead | Nominated | |
| Charlotte Gray | 2002 | Satellite Award for Best Supporting Actor in a Motion Picture, Drama | Nominated | |
| The Elephant Man | Tony Award for Best Actor in a Play | Nominated | |
| The Pillowman | 2005 | Tony Award for Best Actor in a Play | Nominated | |
| The Coast of Utopia | 2007 | Drama Desk Award for Outstanding Featured Actor in a Play | Nominated | |
| The Good Shepherd | Silver Berlin Bear for Outstanding Artist Contribution | Won | |
| The Coast of Utopia | Tony Award for Best Featured Actor in a Play | Won | |
| Arcadia | 2011 | Tony Award for Best Featured Actor in a Play | Nominated | |
| Spotlight | 2016 | Independent Spirit Robert Altman Award | Won | |
| Screen Actors Guild Award for Outstanding Performance by a Cast in a Motion Picture | Won | |
| Harry Clarke | 2018 | Drama Desk Award for Outstanding Solo Performance | Won | |
| The Morning Show | 2020 | Critics Choice Television Award for Best Supporting Actor in a Drama Series | Won | |
| Dorian Award for Best Supporting TV Performance – Actor | Nominated | |
| Primetime Emmy Award for Outstanding Supporting Actor in a Drama Series | Won | |
| Screen Actors Guild Award for Outstanding Performance by a Male Actor in a Drama Series | Nominated | |
| 2022 | Screen Actors Guild Award for Outstanding Performance by a Male Actor in a Drama Series | Nominated | |
| Primetime Emmy Award for Outstanding Supporting Actor in a Drama Series | Nominated | |
| 2024 | Critics Choice Television Award for Best Supporting Actor in a Drama Series | Won | |
| Golden Globe Award for Best Supporting Actor – Series, Miniseries or Television Film | Nominated | |
| Primetime Emmy Award for Outstanding Supporting Actor in a Drama Series | Won | |
| Screen Actors Guild Award for Outstanding Performance by a Male Actor in a Drama Series | Nominated | |
| Screen Actors Guild Award for Outstanding Performance by an Ensemble in a Drama Series | Nominated |
| 2025 | Golden Globe Award for Best Supporting Actor – Series, Miniseries or Television Film | Pending | |
| Jay Kelly | Capri Hollywood International Film Festival Award for Best Ensemble Cast | Won | |