When i think of elfen lied i imideatly think of Deadman Wonderland and Mirai nikki.
I don't watch many series like that since i am a bit disgusted 의해 blood. But if 당신 의해 chance haven't seen those 2, then i can highly recommend them! ;D
i think Higurashi no naku koro ni is like elfen lied. Im not that sure though cause i only saw a trailer of it but it looked interesting and might just be the thing 당신 are looking for. ;)
Monster - One of my 상단, 맨 위로 favorites, great mystery drama. Very smart.
Higurashi no Naku Koro ni (When They Cry) - A great psychological murder mystery series. There's a 초 season that explains a lot.
Now and Then, Here and There - Very sad story. Kids are forced to become soldiers in the future.
Mushishi - My 가장 좋아하는 anime. It's a very surreal fantasy/drama. The series is episodic, (each episode tells a different story), so some of the episodes may have a sad ending. It is highly recommended.
If 당신 want me to send a link on where to watch them, just let me know.