|Fog Over Frisco (1934) [Arlene Bradford]: Killed by her accomplices after she attempts to go straight. (Thanks to Tracey)
Of Human Bondage (1934) [Mildred Rogers]: Dies (off-screen) of tuberculosis (changed from syphilis in the original novel). Her body is not shown; her death is implied by showing the doctor tear up her medical chart after leaving her room. (Thanks to Mac)
Dark Victory (1939) [Judith Traherne]: Dies of a brain tumor; the movie ends by fading out on a close-up of her face on her deathbed.
The Letter (1940) [Leslie Crosbie]: Stabbed in the stomach by Gale Sondergaard in an outdoor garden, while Gale's henchman restrains Bette. (The henchman's back blocks our view of the action.)
In This Our Life (1942) [Stanley 'Stan' Timberlake Kingsmill]: Killed in a car crash/explosion while fleeing from the police. (Thanks to Adam and Tracey)
A Stolen Life (1946) [Kate Bosworth/Patricia Bosworth]: Playing a dual role as twin sisters, "Patricia" is drowned in a boating accident. ("Kate" survives the movie.)
Beyond the Forest (1949) [Rosa Moline]: Dies of complications from a fever following a (self-induced) miscarriage, when she overexerts herself by trying to make her way to the train station instead of getting medical treatment. We see her staggering towards the station, and her body is shown lying on the ground after the train passes. (Thanks to Patre)
Alfred Hitchcock Presents: Out There--Darkness (1959) [Miss Fox]: Killed by James Congdon. (Thanks to John)
Dead Ringer (Dead Image) (1964) [Margaret DeLorca/Edith Phillips]: Playing a dual role as twin sisters, "Margaret" is shot in the head (off-screen) by "Edith," who then arranges the scene to look like a suicide so that she can take over Margaret's identity. Except for a couple of close-ups and in the subsequent morgue scene, the corpse is obviously played by a double and not Bette herself (since the "other" Bette is still on-screen throughout the identity-switching sequence).
Gunsmoke: The Jailer (1966) [Etta Stone]: Shot to death by Amanda Blake as Bette is about to shoot James Arness. (Thanks to John)
Burnt Offerings (1976) [Aunt Elizabeth]: Dies of a heart attack or stroke (it's unclear exactly which it is). (Thanks to Keenan)
Right of Way (1983) [Mini Dwyer]: Commits suicide, along with James Stewart, by carbon monoxide poisoning by letting the car engine run in the closed garage. We last see them sitting in the car before their deaths; their bodies are not shown afterwards. (Thanks to John)