| Year | Association | Category | Nominated work | Result |
| 1969 | Golden Globe Awards | Best Supporting Actor – Motion Picture | For Love of Ivy | Nominated |
| 1990 | American Comedy Awards | Funniest Supporting Actor in a Motion Picture | The Fabulous Baker Boys | Nominated |
| National Society of Film Critics Awards | Best Supporting Actor | Won |
| 1992 | Golden Globe Awards | Best Actor – Miniseries or Television Film | Without Warning: The James Brady Story | Won |
| Primetime Emmy Awards | Outstanding Lead Actor in a Miniseries or a Movie | Won |
| 1993 | Outstanding Supporting Actor in a Miniseries or a Movie | The Positively True Adventures of the AllegedTexas Cheerleader-Murdering Mom | Won |
| 1994 | Golden Globe Awards | Best Supporting Actor – Series, Miniseries or Television Film | Won |
| 1995 | CableACE Awards | Actor in a Drama Series | The Outer Limits | Nominated |
| Primetime Emmy Awards | Outstanding Guest Actor in a Drama Series | Nominated |
| 1996 | Outstanding Lead Actor in a Miniseries or a Movie | Kissinger & Nixon | Nominated |
| 1997 | Golden Globe Awards | Best Actor – Miniseries or Television Film | Losing Chase | Nominated |
| Primetime Emmy Awards | Outstanding Lead Actor in a Miniseries or a Movie | Hidden in America | Nominated |
| Outstanding Supporting Actor in a Miniseries or a Movie | The Second Civil War | Won |
| Satellite Awards | Best Actor – Miniseries or Television Film | Hidden in America | Nominated |
| Screen Actors Guild Awards | Outstanding Performance by a Male Actor in a Miniseries or Television Movie | Nominated |
| 1999 | Primetime Emmy Awards | Outstanding Supporting Actor in a Miniseries or a Movie | Inherit the Wind | Nominated |
| 2000 | Outstanding Lead Actor in a Miniseries or a Movie | Barnum | Nominated |
| Satellite Awards | Best Actor – Miniseries or Television Film | Nominated |
| 2002 | Primetime Emmy Awards | Outstanding Lead Actor in a Miniseries or a Movie | We Were the Mulvaneys | Nominated |
| 2007 | Outstanding Guest Actor in a Comedy Series | My Name Is Earl | Nominated |
| 2008 | Grammy Award | Best Spoken Word Album | An Inconvenient Truth | Won |
| 2009 | Primetime Emmy Awards | Outstanding Guest Actor in a Comedy Series | Desperate Housewives | Nominated |
| 2010 | Outstanding Guest Actor in a Drama Series | The Closer | Nominated |
| 2011 | Gotham Awards | Best Ensemble Performance | The Descendants | Nominated |
| Primetime Emmy Awards | Outstanding Guest Actor in a Drama Series | Brothers & Sisters | Nominated |
| 2012 | Broadcast Film Critics Association Awards | Best Cast | The Descendants | Nominated |
| Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture | Nominated |
| 2014 | Critics' Choice Television Awards | Best Guest Performer in a Drama Series | Masters of Sex | Nominated |
| Primetime Emmy Awards | Outstanding Guest Actor in a Drama Series | Nominated |
| 2015 | Nominated |