Adult/violent/serious animations? That is my field of specialization.

(second world war drama, like Grave of the Fireflies)

(violent fantasy martial arts, like a serious Dragonball with blood)
Expelled from Paradise:

(not that dark though the concept of uploading the minds of humanity into a mainframe is rather terrifying)

(World War 3, enough said)
Perfect World of Kai (silly title for an adult serious film):
4 Mamoru Oshii's films:
1) Ghost in the Shell:

(cyborgs, cyberpunk, violent, serious, emotionally distant)
2) Ghost in the Shell 2:

(really cr*ppy poster though, cyberpunk, violent, serious, emotionally distant, the same as GitS)
3) Patlabor The Movie:

(very impressive film, the plot is a mystery thriller and everything is strictly adult)
4) Patlabor 2:

(science fiction political thriller, has giant robots but that's standard in Japanese science fiction fare}
Patlabor 3 (weaker than the first 2 but still pretty good, not directed by Oshii anyway):
Satoshi Kon's films:
1) Paprika:

(psychological science fiction film, think of Inception (2010) but actually good, since inception is just a second rate copy of Paprika)
2) Perfect Blue:

(psychological thriller, think of Hithcock but animated)
3) Millennium Actress:

(sublime drama film)
PMMM's film trilogy (looks childish at the beginning but it gets dark really fast and goes really down the darkness pit)

(dark fantasy tragedy, lots of pink as well)
Memories:

(collection of artistic short films, including a horror animated short at the beginning, the brilliant Magnetic Rose)
Mindgame:

(Masaki Yuasa's film, it's not among his best works but very impressive pscyhological action/drama experimental animation)
Also, Miyazaki's movies aimed at teenagers besides Princess Mononoke is Nausicaa and he made two movies aimed at middle aged adults: Porco Rosso and Wind Rises.
And, finally the best one: the masterpiece of fanservice animation,
GUNBUSTER

(full of explosions, heavy drama, cute girls, the ultimate OVA anime, a classic for the ages)
I can recommend many more other movies if you want.