I don't know if I have a favorite anime, I know I have many favorites, but I'll throw out one that I recently started and that I think is a great one! Casshern Sins. As of now, it takes the cake for the most depressing anime I've seen. It's set in (of course) an apocalyptic world inhabited mainly by robots with a dying human race. The world is plagued by a mysterious entity known as 'the Ruin', which causes robots to slowly rust away and die. What's interesting is that this mess was caused by the main character, who is completely oblivious to what he has done due to him losing his memory.
It's very interesting, it may sound cliched but give it a chance! It has great music, art and voice acting!