ajlsdfklafdfjd I love Monster. ;3;
Clannad (and Clannad After Story)
I've seen almost all the series that have been suggested so far, and Monster is a great choice if you want something deep and psychological.
It has lots of characters and a very wonderful story ( which is a bit like a puzzle; there are some episodes which seem irrelevant, but they introduce characters who are useful later on ) . Each and every character, even the most minor one, has a role in later episodes and they turn up very unexpectedly. It's basically a psychological thriller / horror, but it was written for an adult audience so it's quite dark and has some violence / nudity. It's also perfect in case you're not familiar with anime, since most of the characters are German ( a few are from Russia and the Czech Republic ) and only the main character is Japanese. The characters actually do sound and look German, and they give off a very Western feel which is rare in Japanese works.
The art looks more realistic than anime-like and character designs are very detailed- they all look extremely different from each other. Apparently the German which is spoken and written in the background is also correct, so the mangaka did his research. :3