|Quo Vadis? (1951) [Nero]: Stabbed in the chest by Rosalie Crutchley, at his own request, when he can't bring himself to commit suicide; he dies in her arms shortly afterwards. (Thanks to Mike and Jeffrey)
Blackbeard's Ghost (1968) [Captain Edward 'Blackbeard' Teach]: Plays the ghost of the legendary pirate. (In real life, Teach was killed during a battle with the British Navy, but I don't know whether the movie mentions the circumstances of his death.)
Ashanti (Ashanti: Land of No Mercy) (1979) [Suleiman]: Shot to death by Michael Caine. (Thanks to Mathew)
Animal Farm (1999) [Old Major]: Providing the voice of a pig (using both animatronics and live animals with Peter's voice dubbed in), he dies of old age/natural causes.
The Bachelor (1999) [Granddad James Shannon]: Dies (off-screen) of old age/natural causes; we learn of his death afterwards when his grandson (Brendan Fraser) gets the news.