|An American Tragedy (1931) [Roberta 'Bert' Alden]: Presumably accidentally drowned when the boat capsizes while she's out boating with Phillips Holmes (who had intended to kill her before the accident took the decision out of his hands). (I haven't seen this version, but I have seen Shelley Winters' death in the 1951 remake A Place in the Sun.)
Madame Butterfly (1932) [Cho-Cho San]: Presumably commits suicide. (I haven't seen this version, but I'm vaguely familiar with the basic story.)
You Only Live Once (1937) [Joan Graham]: Shot in the back when a policeman fires on the getaway car, she dies in Henry Fonda's arms shortly afterwards as he carries her through the woods.
Les Miserables (1952) [Fantine]: Presumably dies of tuberculosis. (I haven't seen this version, but I'm familiar with the story.)
Summer Wishes, Winter Dreams (1973) [Mrs. Pritchett]: Dies of a heart attack while walking along the sidewalk with her daughter (Joanne Woodward).
Damien: Omen II (1978) [Aunt Marion]: Reportedly dies of a heart attack after being frightened by the crow that acts as Jonathan Scott-Taylor's guardian. (I haven't seen this movie myself.) (Thanks to Robert)
Beetlejuice (1988) [Juno]: Plays a ghost who works in the afterlife's bureaucracy; her original cause of death isn't actually specified in the movie, but it's implied to be throat cancer (based on her chain-smoking and the gag in which her cigarette smoke comes out of her tracheotomy incision).