I was going to call this Thinking Man's Anime, but that's sexist. I want to include women as well.

So what am I talking about? I am talking about an anime series or movie which makes the viewer think. In other words, you have to utilize your brain; either to follow the story or to devise the meaning.

I will start off with two:

Casshern Sins. Robotic beings are fighting each other as they face extinction on Earth. But it is much more than action. Casshern meets a variety of individuals who see life differently from one another. This raises questions as to what the nature of existence is, as well as the purpose. Particularly, I like the character Ringo. She's a little girl android who even though realizes she like everyone else is dying, still sees the world as a wonderful, beautiful place.

Boogiepop Phantom. There's no real philosophical issues here. But there is a very complex story told out of chronological order. You need to really expend mental energy, as well as rewatching episodes, to follow what is going on. But it is worth it, especially if you like your anime dark.

Your turn.