The Plunderers (1960) [Rondo]: Shot in the back by Dolores Hart, after John pulls a knife on Jeff Chandler. (Thanks to Gordon)
War Hunt (1962)[Private Raymond Endore]: Slain by his own squadmates when his "war-hunting" threatens to break a cease-fire.
The Appaloosa (Southwest to Sonora) (1966) [Chuy Medina]: Shot to death with a distance rifle by Marlon Brando, after Marlon tricks him into giving away his position. (Thanks to Gordon and Brian)
The Intruders (1970) [Billy Pye]: Shot by one of the Younger Brothers' gang, after John shouts a warning to Don Murray; he dies shortly after being taken back to town. (Thanks to Brian)
Mitchell (1975) [Walter Deaney]: Killed in an explosion when his dune buggy crashes while being chased by Joe Don Baker. (Note: I've only seen the Mystery Science Theater 3000 version of this movie, in which John's death scene is cut out, but I've read about the 'missing' scene in several on-line discussions of the movie.)
Mark Strikes Again (Mark colpisce ancora) (1976) [Altman]: Accidentally machine-gunned by one of his officers, who was trying to kill Franco Gasparri. (Thanks to Andrea)
The Cynic, the Rat & the Fist (Il Cinico, l'infime, il violento) (1977) [Frank Di Maggio]: Shot in the chest by Tomas Milian during a big shoot-out between the rival gangs. (Thanks to Andrea)
Shalimar (The Deadly Thief) (1978) [Colonel Columbus]: I remember that he was killed in this movie, but it's been so long since I've seen it that I've forgotten the circumstances.
Battle Beyond the Stars (1980) [Sador]: Goes down with his dreadnaught when Darlanne Fluegel and Richard Thomas crash a smaller warship into John's vessel (with Darlanne and Richard ejecting at the last moment). (Thanks to Tal)
Welcome to Spring Break (Nightmare Beach) (1988) [Strycher]: Shot in the chest by Luis Valderrama as John is about to shoot Nicholas de Toth; John is then dragged behind a motorcycle. (Thanks to Andrea)
My Mom's a Werewolf (1989) [Harry Thropen]: Stabbed in the chest (while he's in his werewolf form) with a silver fork attached to a staff by Tina Caspary while John is about to attack Susan Blakely (in her werewolf form). (Thanks to Andrew)
Aftershock (1990) [Oliver Quinn]: Stabbed in the stomach with a knife throw by Jay Roberts Jr while John shoot him at the end of the fright.
Hellmaster (1992) [Professor Saxon]: Burned to death (though I don't know the details).
Jonathan of the Bears (Jonathan degli orsi) (1993) [Fred Goodwin]: Shot to death by Franco Nero. (Thanks to Andrea)
Trapped Ashes (2006) [Leo]: Commits suicide (off-camera) by shooting himself in the head, some time before the story begins. It's revealed at the end of the movie that all the characters telling their stories are already ghosts; his death is shown in a flashback when Henry Gibson reminds him how his story actually ended. We only see the blood splatter on the wall in the flashback.
Deaths in Television
The Dick Powell Theatre: A Time To Die (1962) [Nick Giller]: Found dead in his darkened apartment with a bloody wound on his neck (presumably stabbed) by Dick Powell, who had come to kill him and found John's criminal rivals had beaten him to it. (Thanks to Brian)