|Shopping (1994) [Billy]: Killed in a car crash and/or shot to death when he crashes a stolen car into a mall window as the police fire on the car. (I don't know whether it was the crash or the gunfire that killed him.) (Thanks to M.)
Gattaca (1997) [Jerome Eugene Morrow]: Commits suicide by burning himself in an incinerator. (Thanks to Elizabeth and Jovita)
Midnight in the Garden of Good and Evil (1997) [Billy Carl Hanson]: Shot to death (off-screen) by Kevin Spacey in Kevin's study. His body is shown afterwards when John Cusack arrives in the middle of the police investigation.
Final Cut (1998) [Jude]: Stabbed in the back and neck; the movie opens with his funeral and the murder is shown in flashback. (Thanks to M. and Liz)
Immortality (The Wisdom of Crocodiles) (1998) [Steven Grlscz]: Shot in the chest by Elina Lowensohn; he dies shortly afterwards due to her refusal to let him drink her blood, which would heal him. (Thanks to M.)
The Talented Mr. Ripley (1999) [Dickie Greenleaf]: Beaten to death with an oar by Matt Damon while out in a boat with him; Matt then dumps Jude's body overboard.
AI: Artificial Intelligence (2001) [Gigolo Joe]: Playing an android, he is presumably dismantled (off-screen) after being seized by the authorities. (Thanks to M.)
Road to Perdition (2002) [Harlen Maguire]: Shot in the back by the mortally-wounded Tom Hanks while Jude is menacingly approaching Tom's son (Tyler Hoechlin).
Cold Mountain (2003) [W.P. Inman]: Shot in the stomach by Charlie Hunnam; he dies in Nicole Kidman's arms shortly after riding back to her. (Thanks to Nick, Emily and M.)
Sleuth (2007) [Milo]: Shot in the stomach by Michael Caine; he then falls down an elevator shaft. (Thanks to ND, Hamish, and Thierry)