I have the feeling that I'll be the odd ball out here seeing as many already posted intros I like a lot.
Watamote - A powerful metal track for the intro that has a lot of interesting quirks and animation that goes well with it especially for the slice of life cringe comedy it is especially.
Although one of the most creative of outros I've seen out of anime has got to be the outro itself. It works and fits so well for the overall tone of the show/series. The anime isn't for everybody but I cannot get enough of this creative direction on it.
But one I'm surprised I didn't see mentioned was Fullmetal Alchemist's opening for Brotherhood.