I loved 'The Last Love Song of the Planet Earth' AKA 'Saikano; She the Ultimate Weapon' which was incredibly dark and twisted with a bit of humour. It's classified as a 'Shoujo' which means girl's anime/comic but it's still got that psychological impact that will leave you muttering, 'What did I just watch...?' It's about a girl who the government turns into a super weapon that is constantly evolving and the angst of being a teenager.
Also, 'Wolf's Rain' is pretty good. It's a post-apocalypse sort of thing and follows lore about how Wolves will lead the way into heaven. I found it beautifully drawn and I couldn't get enough of it.
Beserk is very violent and bleak. It is a medieval anime that follows the life of a mercenary named Guts. Guts carries a big sword and an even bigger chip on his shoulder.
High School of the Dead is a zombiefest with big boobies and bigger guns. But it's got a darker element to it, following the lives of a few high school students from the start of the end of humanity.
Casshern Sins is another dark and very primordial anime. It follows Casshern as he wakes up and finds everything he knows to be destroyed and many people's reactions to his sudden appearance makes him believe that he's the one that caused the end of the world.
If you liked Inception, then I recommend 'King of Thorn'. A very odd movie, just one installment, but it's about trying to survive the end of humanity where a mysterious plague turns people into statues. It follows the half of a set of twins, both girls are survivors but only one gets her name drawn for a lottery that will send her into a deep cryogenic sleep. Upon awakening, she realizes that the world has changed and things aren't exactly how they seem.
