| Year | Movie | Award | Category | |||
| 2005 | A History of Violence | Online Film Critics Association | Best Supporting Actor | |||
| 2005 | A History of Violence | New York Film Critics Circle | Best Supporting Actor | |||
| 2005 | A History of Violence | Los Angeles Film Critics Association | Best Supporting Actor | |||
| 2005 | A History of Violence | Academy of Motion Picture Arts and Scie | Best Supporting Actor | |||
| 1999 | Sunshine | Genie Awards | Best Supporting Actor | |||
| 1987 | Broadcast News | Academy of Motion Picture Arts and Scie | Best Actor | |||
| 1986 | Children of a Lesser God | Academy of Motion Picture Arts and Scie | Best Actor | |||
| 1986 | Children of a Lesser God | Hollywood Foreign Press Association | Best Performance by an Actor in a Motion Picture - Musical or Com | |||
| 1985 | Kiss of the Spider Woman | Academy of Motion Picture Arts and Scie | Best Actor | |||
| 1985 | Kiss of the Spider Woman | National Board of Review | Best Actor | |||
| 1985 | Kiss of the Spider Woman | Los Angeles Film Critics Association | Best Actor | |||
| 1985 | Kiss of the Spider Woman | Cannes Film Festival | Best Actor | |||
| 1985 | Kiss of the Spider Woman | British Academy of Film and Television | Best Actor | |||
| 1980 | Altered States | Hollywood Foreign Press Association | New Star of the Year - Male |
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