| Year | Award | Category | Work | Result |
| 1987 | New York Film Critics Circle Award | Best Supporting Actor | Full Metal Jacket | Nominated |
| 1994 | Independant Spirit Award | Best Male Lead | Household Saints | Nominated |
| 1996 | Golden Space Needle Award | Best Actor | The Whole Wide World | Nominated |
| Seattle International Film Festival | Best Actor | Won |
| 1997 | National Society of Film Critics Award | Best Actor | Nominated |
| 1998 | Lone Star Film & Television Award | Best Actor | Won |
| Primetime Emmy Awards | Primetime Emmy Award for Outstanding Guest Actor in a Drama Series | Homicide: Life on the Street | Nominated |
| Saturn Awards | Best Supporting Actor | Men in Black | Won |
| Blockbuster Entertainment Award | Favorite Supporting Actor | Nominated |
| 2001 | Blockbuster Entertainment Award | Favorite Supporting Actor | The Cell | Nominated |
| Fangoria Chainsaw Awards | Best Supporting Actor | Won |
| MTV Movie Award | Best Villain | Nominated |
| 2005 | Satellite Award | Best Actor – Television Series Drama | Law & Order: Criminal Intent | Nominated |
| Stockholm Film Festival Award | Best Actor | Thumbsucker | Won |
| 2009 | Nashville Film Festival Award | Best Actor | The Narrows | Won |
| 2012 | Sitges Film Festival | Best Actor | Chained | Won |
| 2015 | Teen Choice Awards | Teen Choice Award for Choice Movie Villain | Jurassic World | Nominated |
| EWwy Awards | Best Supporting Actor in a Drama Series | Daredevil | Nominated |
| IGN Summer Movie Awards | Best TV Actor | Nominated |
| Best TV Villain | Nominated |
| 2016 | Saturn Award | Best Supporting Actor on Television | Nominated |
| 2018 | IGN Summer Movie Awards | Best Dramatic TV Performance | Nominated |
| 2022 | Critics' Choice Super Awards | Best Villain in a Series | Hawkeye | Nominated |
| 2025 | Astra TV Awards | Best Supporting Actor in a Drama Series | Daredevil: Born Again | Nominated |
| Critics' Choice Super Awards | Best Villain in a Series | Nominated |