The most moving anime.

[no one]

If you are looking for a good plot, some mystery and doesn't mind a bit of crappy artwork then go watch higurashi no Naku Koro ni. It's a classic.

If you want action, gore and some yuri on the side, Ga-Rei: Zero is for you. Not as complex as higurashi in term of plot though.

If you are tired of the shounen genre but still want some action, check out Shiki. Most definitely recommended if all of those twilight movies made you lose your faith in vampire fiction

If you need something a bit more peaceful, more episodic and great originality then give Mushishi a try.