Andante from Rachmoninov's Sonata in G Minor for Cello and Piano. Purely instrumental music never strikes an emotional chord with me often, but this is something else. I don't know what it was inspired by, but it just sounds like a life falling apart... Maybe not something quite so depressing though. Either way, the climax near the end, with the piano ascending and then descending delicately destroys me, and I love it.
In contrast of musical era perhaps, Subterranean Homesick Alien by Radiohead. Such a beautiful portrayal of dissociation, disconnection, desperation. Not really sure how else to describe it.