I can't dredge up many "horror" titles off of the top of my mind (that got to me, anyway). However, Perfect Blue would have to top that non-existent list, had it existed. Directed by Satoshi Kon (came out like 1997 or '98, so it's kind of old by now), the protagonist is the head of a female pop group, who has aspirations of reaching TV/movie land. As she takes steps towards changing careers, she finds out her biggest fan doesn't like this and strange, disturbing things begin happening to her that challenge her sanity and being-alive-status. An excellent movie to watch in the dark, when you're all by your lonesome.
Satoshi Kon is also the director and/or creator (something in there) of Millennium Actress, Paprika, Paranoia Agent, and Tokyo Godfathers. I love 'em all. He is an artist when it comes to mind-bending works.