Perfect Blue - This is a full-length feature, but yes, it is very disturbing. Enjoy.
Boogiepop Phantom - The creepiest anime I've seen, even if it doesn't necessarily fit directly into the horror genre. Everything from the hazy, lo-fi, ridiculously dark animation to the bizarre character stories makes it wonderfully unsettling. Although, the plot is ambiguous. The vignettes that make up the story interconnect but they don't all clearly resolve. Then again, isn't that scarier?
I thought the first season of Higurashi was pretty scary too, although when I watched it I couldn't legally buy alcohol, so I promise nothing (it's been six years since that show aired?!).
Off-topic: Overall, I wish studios would try horror more often. No, not gore. I think we've got that covered. No, not people fighting monsters, we've got that covered too. Horror. Anime has an excellent potential for this (character-focused stories, can't use jump scares, etc.), but I can't think of any studios who even bother to try. Nearly every show I see advertised as "horror" turns out to be nothing more than endless sexualized violence (hello, Elfen Lied).
I understand that if I got the appeal of that (and if it weren't so boring), it wouldn't annoy me quite so much. Still, it's depressing when that "Null Carrier" episode of Dennou Coil is creepier than your horror anime.
[sub]Or am I using the wrong definition of the word "horror"?[/sub]