Messed-up & Weird Rating Comment
Akira (movie) Good These are series and movies that I consider to be bizarre, shocking, graphic, insane, or otherwise out of the ordinary -- the opposite of a cute, feelgood, turn your brain off, cry your eyes out anime. "Weirdness" can be achieved through several means, like through comedy (Excel Saga, PaniPoni Dash, FLCL), violence (Texhnolyze, Berserk, NTHT), abstract imagery (Night on the Galactic Railroad, Haibane Renmei), psychological intensity (Paranoia Agent, Death Note) or other elements. For hentai included on the list, I'm mainly considering which series are deviant by hentai standards--series can't make this list simply by having explicit sex scenes or nudity.
Apocalypse Zero (OAV) Worst ever
Aquatic Language (special) Good
Berserk (TV) So-so
Bible Black (OAV) Very good
(The) Big O (TV) Decent
Bludgeoning Angel Dokuro-chan (TV) Good
Cat Soup (OAV) Decent
Code Geass: Lelouch of the Rebellion (TV) Very good
Colorful (TV) Good
Cromartie High School (TV) Good
Daicon films (special) Good
Death Note (TV) Very good
ef: a tale of memories (TV) Excellent
Excel Saga (TV) Excellent
FLCL (OAV) Excellent
Gankutsuou: The Count of Monte Cristo (TV) Very good
Gantz (TV) So-so
Garzey's Wing (OAV) Worst ever (dub), Awful (sub)
Gasaraki (TV) Good
Green Green (TV) Weak
H2O ~Footprints in the Sand~ (TV) Decent
Haibane Renmei (TV) Masterpiece
Higurashi no Naku Koroni Kai (TV) Excellent
Jin-Roh - The Wolf Brigade (movie) Excellent
Kanokon: The Girl Who Cried Fox (TV) So-so
Key the Metal Idol (OAV) So-so
Kirameki Project (OAV) Good
Kodomo no Jikan (TV) Good
Kujira no Chōyaku - Glassy Ocean (movie) Very good
Magical Shopping Arcade Abenobashi (TV) Excellent
Mermaid Forest (TV) Good
(The) Mouse and His Child (movie) Excellent
Neon Genesis Evangelion (TV) Excellent
Neon Genesis Evangelion: The End of Evangelion (movie) Excellent
Nerima Daikon Brothers (TV) Very good
NieA_7 (TV) Very good
Night on the Galactic Railroad (movie) Very good
Noein - to your other self (TV) Good
Now and Then, Here and There (TV) Masterpiece
Pani Poni Dash! (TV) Excellent
Paranoia Agent (TV) Masterpiece
Platonic Chain (TV) Good
(Le) Portrait de Petite Cossette (OAV) Excellent
Princess Tutu (TV) Excellent
Puni Puni Poemy (OAV) Decent
Revolutionary Girl Utena: The Movie Very good
Sayonara, Zetsubou-Sensei (TV) Excellent
School Days (TV) Very good
Seraphim Call (TV) Good
Serial Experiments Lain (TV) Excellent
Shadow Star Narutaru (TV) Decent
Texhnolyze (TV) Excellent
Uta∽Kata (TV) Very good
Welcome to the NHK (TV) Very good
When They Cry - Higurashi (TV) Excellent
A Wind Named Amnesia (movie) Very good
Yume Tsukai (TV) Good
Zoku Sayonara Zetsubō Sensei (TV) Excellent