What are the best Horror animes?

Corpse Party

For psychological horror, Satoshi Kon is hard to beat! Try Paranoia Agent, Paprika, oder Perfect Blue! :)

Shiki
Hell Girl
Higurashi No Naku Koro Ni
Umineko No Naku Koro Ni
Ghost Hunt
xxxHolic
Le Portrait de Petite Cossette
Monster
Puella Magi Madoka Magica (picture)
Ookami Kakushi
11 Eyes (Kind of-ish?)
Shingeki no Kyojin
Deadman Wonderland
Mirai Nikki

Corpse Party

I really like higurashi no naku koro ni.

If Du liked Elfen Lied and Another, then maybe:
Umineko no Naku Koro ni (and Higurashi, like what others are suggesting)
Shiki
Gantz
Serial Experiments Lain
Claymore
Blood+ (or Blood-C)
Tasogare Otome x Amnesia
Denpa Teki na Kanojo

I can't think of any other ones that haven't been gepostet yet. >.< I agree with most of the series on Katherine's answer.

Elfen Lied
Hellsing Ultimate
Highschool of the Dead

Mirai Nikki
shiki
Higurashi no naku koro ni (kai)
umineko no naku koro ni
madoka magica
h.o.t.d
Btooom! (kinda)
11eyes
deadman wonderland (i didn't like it thou)
#$** girl