I was going to recommend Berserk myself since it seems to fit that horror role quite well though, it's super crazy lol! The only other anime I can think of is Ghost Hunt which I found to be quite good for horror (I'm a wimp so I scare easy). I would actually really recommend checking that one out to be honest.
I was going to recommend Mushi-shi since it has its fair share of creepy, sad, and depressing moments that fit the horror bill imho.
The best horror imho is that which has a lot of buildup, good atmosphere, lots of mystery, and little to no gore or violence with generally smart and or mature characters. I think we can do a better job of finding something along those lines, I think.