A short list of all the anime I've seen that can possibly bring tears to the eyes or just mess you up mentally...
School Days <-- oh ya if ya dont know... dear lord prepare yourself
Phantom ~Requiem for the Phantom~
Da Capo all story arcs except for Da Capo
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Clannad the Movie <-- unlike the series it wasn't a freakish dream...
Kannon <-- after 2-3 episodes just completely hits sad mode
Tsubasa Reservoir Chronicles in a sense
Akagi
Death Note
Gantz <-- lots of people dying that didnt need to
Gyakkyou Burai Kaiji
Kiba <-- everybody that u wanna see die.. dies...
H2O <-- lots of abuse
Heroic Age <-- rough ending... good story
Higurashi no Naku Koro ni <-- tons of adolescent death and murdering in all story arcs
I's Pure + I's Pure OVA
Ima, Soko Ni Iru Boku <-- after 1 episode it all gets messed up
Jigoku Shoujo all story arcs <-- after the first 2 episodes its 3 seasons worth of messed up sadness
Juuousei <-- tragic
Gundam 00 + 00 Season 2 <-- giant robots, explosions, tragedy
Kenpuu Denki Berserk <-- classic tragedy
Cowboy Bebop <-- classic tragedy
Kimi ga Nozomu Eien + 2nd season OVA <-- if you just dont know... prepare for some tears...
Koi Kaze <-- incest? check... tragedy + mind f'ck... check
Macross Frontier <-- artwork + tears it brings all the goodies
Mai-HiME <-- hot girls that bring tears to your eyes
Mnemosyne: Mnemosyne no Musume-tachi <-- in a sense... brutal
Monster <-- yup just like the title its pretty crazy
Mugen no Juunin <-- amazing art work + samurai + brutal story = lots of sadness
Rah Xephon <-- Evangelion'esque sadness... pretty moving story
Seikai no Senki all story arcs <-- moving story line pretty tragic in a lot of episodes
Shigofumi: Stories of Last Letter <-- pretty good story here about the last wishes of the dead
Shikabane Hime Aka + Kuro <-- ranks among the top when you mention tragedy and sadness
Shinreigari: Ghost Hound <-- some dark stuff involving kids
Shingetsutan Tsukihime <-- classic tragedy very very moving story
Blood the Last Vampire and Blood+ Movie <-- tragic the entire way
Suzuka <-- good ol fashioned drama and sadness... the manga was more brutal
Neon Genesis Evangelion <-- if ya havent seen it... you might just be too young
Tokko <-- bloody, brutal, sad... badly needs a 2nd season
Wolf's Rain <-- adult swim classic
Tengen Toppa Gurren Lagan aka TTGL <-- you will laugh you will cry then cry some more then shout F'ck Yeah!
Kurozuka <-- bringin the roots back from the original Aeon Flux... samurai? check ninjas? check tragic messed up story? oh yeah!
Koukyoushi Hen: Eureka Seven - Pocket ga Niji de Ippai <-- one of the new ones alternate story of Eureka 7... it brings the tears thats for damn sure
^HAS NOT BEEN UPDATED IN 11 MONTHS LOL