All the above are grim and/or depressing but no one has mentioned 'Kite'. A story of kids turned into assassins, their morality and sense of self stripped away, etc...oh yeah, this is grim. And the director's cut retains some of the harsher violent sex, making this NOT one to share with-well, anyone, really. I kinda liked it when I rented it a while back, so I bought the DVD Dir. cut. Ooops. The animation is very good, but the story just doesn't put that bounce in your step, know what I mean?
Anyway, unless brutality and un-pleasentness are your thing, stick to the mildly depressing Akira, which ends on a high, or Evangelion, which sorta doesn't end...really...I guess...