Awards
| Year | Award | Category | Movie | Result |
|---|---|---|---|---|
| 2011 | Academy of Television Arts and Sciences | Outstanding Lead Actor in a Miniseries or a Movie | Too Big to Fail | Nominated |
| 2011 | Golden Globes | Best Performance by an Actor in a Miniseries or Motion Picture Made for Television | Too Big to Fail | Nominated |
| 2005 | Academy Awards | Best Supporting Actor | A History of Violence | Nominated |
| 2005 | Los Angeles Film Critics Association | Best Supporting Actor | A History of Violence | Won |
| 2005 | New York Film Critics Circle | Best Supporting Actor | A History of Violence | Won |
| 2005 | Online Film Critics Association | Best Supporting Actor | A History of Violence | Nominated |
| 1999 | Genie Awards | Best Supporting Actor | Sunshine (2000) | Nominated |
| 1987 | Academy Awards | Best Actor | Broadcast News | Nominated |
| 1986 | Academy Awards | Best Actor | Children of a Lesser God | Nominated |
| 1986 | Golden Globes | Best Performance by an Actor in a Motion Picture - Musical or Comedy | Children of a Lesser God | Nominated |
| 1985 | Academy Awards | Best Actor | Kiss of the Spider Woman (RE) | Won |
| 1985 | British Academy of Film and Television Arts | Best Actor | Kiss of the Spider Woman (RE) | Won |
| 1985 | Cannes Film Festival | Best Actor | Kiss of the Spider Woman (RE) | Won |
| 1985 | Los Angeles Film Critics Association | Best Actor | Kiss of the Spider Woman (RE) | Won |
| 1985 | National Board of Review | Best Actor | Kiss of the Spider Woman (RE) | Won |
| 1980 | Golden Globes | New Star of the Year - Male | Altered States | Nominated |
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