- Won: Best Supporting Actor – Motion Picture for The Untouchables (1987)
ALMA Awards:
- Won: Outstanding Individual Performance in a Crossover Role in a Feature Film for When a Man Loves a Woman (1994)
- Won: Outstanding Latin Movie Actor in a Crossover Role for Just the Ticket (1999)
- Won: Outstanding Latino Cast in a Feature Film for Ocean's Eleven (2001)
- Won: Anthony Quinn Award of Excellence (2005)
- Nominated: Outstanding Actor in a Feature Film for Things You Can Tell Just by Looking at Her (2000)
Independent Spirit Awards:
- Won: Best Male Lead for Things You Can Tell Just by Looking at Her (2000)
- Nominated: Best Supporting Male for Swimming with Sharks (1994)
MTV Movie Awards:
- Nominated: Best Fight for The Untouchables (1987) (shared with Sean Connery and Robert De Niro)
National Society of Film Critics Awards:
- Nominated: Best Supporting Actor for The Untouchables (1987)
Venice International Film Festival:
- Won: Best Supporting Actor for The Untouchables (1987) (shared with Sean Connery)