Movies that present overt violence and gore for the sake of creating a spectacle are generally more likely to anger or offend than really disturb me.
On the opposing side, here are a few movies that have truly gotten under my skin:
Gaslight: A man keeps his wife essentially captive in her own home, systematically manipulating her so that she begins to lose faith in her own
sanity (this is where the term "gaslighting" originated).
Paradise Lost and the related documentaries: Documentaries chronicling the West Memphis 3 incident and the trials that followed. In one portion
of the documentary, the camera follows the father of one of the victims as he surveys the scene of his son's gruesome murder. It is made all the more
eerie by the viewer's established perception that he (the father) may have been the murderer himself. His demeanor is chilling.
What Ever Happened to Baby Jane?: An insane woman whose childhood fame is long gone keeps her disabled sister hostage. This scene is toward the
end of the film, when murder seems impending. The victim realizes her last hope of rescue is gone, and the look of despair (and eventually defeat) on
her face is truly disturbing.
Ingmar Bergman's faith trilogy, particularly
The Silence: Each of the three films is eerie in its own right, but this one is on a different
level. The most memorable portion for me is the primary character's slow process of a natural death. Her doctor is watching over her, and his look of
bewilderment and concern is almost as unsettling as her death is. And that noise is worst of all.