|The Postman (1997) [Bandit 20]: Stabbed to death by Kevin Costner. (Thanks to J. and Robert)
Phoenix (1998) [Joey Schneider]: Killed by Tom Noonan. (Thanks to Gary)
Saving Private Ryan (1998) [Private Irwin Wade]: Shot in the liver during a battle with German soldiers; he dies shortly after the firefight as the rest of the men in his unit try to save him.
It's the Rage (All the Rage) (1999) [Sidney]: Shot to death (off-camera) by Bokeem Woodbine and another police officer outside a video store; the scene ends with the police ordering him to put his hands up, followed by a screen of text informing us of the incident's outcome.
The Gift (2000) [Buddy Cole]: Commits suicide (off-screen) in the hospital; his ghost appears to save Cate Blanchett from Greg Kinnear, but we don't learn until afterwards that Giovanni was already dead when he rescued her.
Heaven (2002) [Filippo]: The final scene shows Giovanni and Cate Blanchett ascending straight up in a helicopter until they disappear from sight; if interpreted literally, they would both presumably die in the inevitable crash shortly after the movie ends (although the scene appears more symbolic). (Thanks to Diahann)
Basic (2003) [Kendall]: Poisoned by Tim Daly; he dies in his hospital room shortly afterwards. (Thanks to Tal)
Masked and Anonymous (2003) [Soldier]: Machine-gunned by soldiers in the street after he gets off the bus; shown through the bus window as Bob Dylan looks out.