|The Eddy Duchin Story (1956) [Marjorie Oelrichs Duchin]: Dies in the hospital shortly after childbirth, with Tyrone Power at her bedside.
Jeanne Eagels (1957) [Jeanne Eagels]: Dies of a heroin overdose. (I haven't seen this movie myself, so I don't know whether her death was depicted on-screen or not.)
Vertigo (1958) [Madeleine Elster/Judy Barton]: Accidentally falls to her death from a church bell tower after being startled by a nun. We only hear her scream; neither the fall nor the body is actually shown. (Kim also appeared to fall from the tower earlier in the film, but that was actually Jean Corbett.)
Of Human Bondage (1964) [Mildred Rodgers]: Dies of syphilis in the hospital, with Laurence Harvey at her bedside. (See also Bette Davis in the 1934 version.)
The Legend of Lylah Clare (1968) [Lylah Clare/Elsa Brinkmann]: Playing a dual role, "Lylah" falls to her death from a staircase when she faints after seeing Lee Meriwether fall from the same staircase; their bodies are showing lying side by side afterwards. "Elsa" later falls to her death when she has an attack of vertigo while on a trapeze during the filming of a movie. (Thanks to Gerardo)
Satan's Triangle (1975) [Eva]: Hanged in an "accident" brought about by Satan's powers. (Thanks to Robert)