|Mystery and Imagination: The Fall of the House of Usher (1966) [Roderick Usher]: Presumably killed when the house collapses around him while he's struggling with his sister (Susannah York). (I haven't seen this version, so I don't know how closely it follows the original story.)
Mystery and Imagination: Dracula (1968) [Dracula]: Presumably stabbed in the chest with a wooden stake by Bernard Archard.
Too Late the Hero (Suicide Run) (1970) [Captain Hornsby]: Machine-gunned by a Japanese guard from the watchtower, as Denholm comes out of the radio hut. (Thanks to Brian)
The House That Dripped Blood (1971) [Charles Hillyer]: Strangled (off-screen) by Tom Adams; we learn of his death afterwards when Joanna Dunham gets a phone call informing her. His body is not shown.
The Vault of Horror (Tales from the Crypt Part II) (1973) [Diltant]: Killed (though I can't recall the circumstances) when Tom Baker destroys his "voodoo portrait" of Denholm.
To the Devil...a Daughter (Child of Satan) (1976) [Henry Beddows]: Burned to death when Christopher Lee casts a spell causing Denholm to spontaneously combust, while Richard Widmark looks on in horror.
Saint Jack (1979) [William Leigh]: Dies of a heart attack in the gentlemen's club; he dies after Ben Gazzara and the others walk him over to the couch and attempt to revive him.
Zulu Dawn (1979) [Colonel Pulleine]: Stabbed in the chest with a spear by a Zulu warrior in Denholm's tent. (Thanks to Stephen)
The Ray Bradbury Theater: The Coffin (1988) [Richard Braling]: Embalmed while still alive after lying down in the automatic coffin.
Indiana Jones and the Kingdom of the Crystal Skull (2008) [Dr. Marcus Brody]: Although he does not appear in this film (as it was made many years after his real-life death), it's revealed that his character from the previous Indiana Jones movies had died off-screen between the movies. (Thanks to Augustin and Tommy)