|The Studio Murder Mystery (1929) [Richard Hardell]: Killed (though I don't know exactly how) by Warner Oland.
Dr. Jekyll and Mr. Hyde (1931) [Dr. Henry Jekyll/Mr. Hyde]: Shot in the chest by police while trying to hold them off in his laboratory. After his death, his body transforms from Hyde back to Jekyll.
The Eagle and the Hawk (1933) [Jerry H. Young]: Commits suicide (though I don't know the exact method). After discovering his body, Cary Grant places his body in his plane and shoots at it to make it look as though Fredric died in combat.
Mary of Scotland (1936) [Earl of Bothwell]: Dies of unspecified causes (presumably a combination of illness and starvation) in his prison cell, after delivering a delirious speech to Alec Craig.
A Star Is Born (1937) [Norman Maine]: Commits suicide by drowning himself in the ocean. We see him swimming out to sea, followed by a shot of a newspaper headline announcing the discovery of his body.
Death of a Salesman (1951) [Willy Loman]: Commits suicide (presumably off-screen) by walking into traffic. (I haven't seen this movie myself, but I'm familiar with the original play.)
Alexander the Great (1956) [Philip of Macedonia]: Stabbed to death by Peter Wyngarde. (Thanks to Glen and Jeffrey)
Inherit the Wind (1960) [Matthew Harrison Brady]: Dies (off-screen) in the hospital, shortly after suffering a heart attack while making a speech in the courtroom. (Thanks to Wilson)