|Othello (1955) [Desdemona]: Smothered by Gordon Heath; she manages to make one final speech to Daphne Anderson before she dies.
The Dupont Show of the Month: Wuthering Heights (1958) [Cathy]: Dies in childbirth.
Blithe Spirit (1966) [Elvira Condomine]: Dies of a heart attack (off-screen), several years before the story begins; she appears as a ghost to Dirk Bogarde throughout the movie after Ruth Gordon holds a seance. (I haven't seen this version, but I have seen Kay Hammond in the 1945 version.)
Holocaust (1978) [Berta Palitz Weiss]: Killed in the gas chamber at Auschwitz. (Thanks to Gordon)
My Life So Far (1999) [Gamma Macintosh]: Dies of hypothermia after walking on thin ice and falling into the water. (Thanks to Gordon)
Sunshine (1999) [Valerie Sors]: Dies (off-screen) in the hospital, shortly after suffering a heart attack; we learn of her death afterwards when her grandson (Ralph Fiennes) comes to visit her and sees her empty bed.
The Gift (2000) [Annie's Granny]: Dies (off-screen) of old age/natural causes, some time before the story begins; she only appears as a vision or ghost to her granddaughter (Cate Blanchett).
Before the Devil Knows You're Dead (2007) [Nanette]: Shot in the stomach by Brian F. O'Byrne during a robbery; she dies in the hospital some time later after her life-support equipment is turned off. (Thanks to Gerardo)