|Boomerang! (1947) [Paul Harris]: Commits suicide by shooting himself in the courtroom.
Tulsa (1949) ['Crude' Johnny Brady]: Killed (off-screen) in a bar brawl; we learn of his death afterwards when Chill Wills gets the news.
Dark City (1950) [Barney]: Strangled and hanged (off-screen) by Mike Mazurki; the scene cuts away just after Mike grabs Ed through a curtain.
Odds Against Tomorrow (1959) [Dave Burke]: Commits suicide by shooting himself in the head, after being wounded in a shoot-out with police; we only hear the gunshot after the camera cuts away. (Thanks to Jim)
The Alfred Hitchcock Hour: Triumph (1964) [Brother Thomas Fitzgibbons]: Shot to death, along with Maggie Pierce, by Tom Simcox as their boat approaches the dock.
Hang 'Em High (1968) [Captain Wilson]: Commits suicide by hanging himself, rather than wait to be killed by Clint Eastwood. (Thanks to Robert and Stephen)