Try maybe Mawaru Penguindrum. It's pretty bizarre and it makes you think. The setting is not dark (it's rather cute and colorful at first glance) but it gets progressively disturbing. No gore, no horror ^^
Might not be mindblowing, but here's some anime that made me think (a few have manga as well)
Mushishi
Pakprika- it's a movie. If you want mind fuckery, you'll definitely get that
Ghost Hound
Boku Dake ga Inai Machi / Erased
Psycho-Pass
Eden of the East
I know you said no horror but Monster is amazing if you want to give it a go.
Blew my mind o:
http://www.mangago.me/read-manga/tamashii_no_futago/
No longer Human is a good one... Too bad the manga banned everywhere online cause of how fucked up it was... I've already read it in my public library, and let me tell you this... I'm a changed person after reading it.
looking for mangas /animes that will make my brain go WTF and leave that annoying empty what-to-do-with-my-life-now feeling. I totally enjoyed xxxholic, dendrobates, those kind of dark but not horror things. all recoms welcomed (๑•ㅂ•)و✧