I'm reading this topic and there's a certain name missing, that being Naoki Urasawa. My favorite anime is Monster, an exact scene-for-scene adaptation of his manga by the same name. Maybe people here have seen it, but I didn't notice that anybody listed it so I'll give a brief summary. It takes place in Germany and basically there's this guy Johan Liebert who had a screwed-up childhood involving neo-nazis and political scandals. He goes on to become a brutal sociopath who goes around mind f*****g everyone and killing people just because he can. This Japanese doctor named Kenzo Tenma gets involved in the whole affair and goes on an excursion across Germany trying to hunt Johan down. Meanwhile he himself is being hunted by the police for crimes he didn't commit, as well as one particularly psycho detective who pursues him with the dedication of a Terminator and refuses to admit, no matter what, that he might be after the wrong guy. Urasawa's also authored some of my other favorite manga--especially 20th Century Boys, a story about some kids who came up with a harmless story about a villain destroying the world, and later when they're adults one of them, under the pseudonym "Friend", takes the "prophecies" they wrote and actually attempts to carry them out. When the good guys try to stop him he frames them as the villains and makes himself out to be the world's hero. Master Keaton is also really good, as is Pluto, a darker and more mature retelling of a famous story arc from Osamu Tezuka's Astro Boy, and his latest manga Billy Bat is some crazy-ass metafiction and the only manga I can think of to have both ninias AND Jesus appear in it at different points in the story. Can't get much better than that.
Wow, really rambled on there. Uh, some of my other favorite anime are Fullmetal Alchemist and Brotherhood, Eureka Seven, Gungrave, Clannad, One Piece, Dragonball Z, Yu Yu Hakusho, Darker than Black, Baccano!, Hunter X Hunter, and, uh, many others. Some other favorite mangas are Berserk (tremendous blood and gore AND an intriguing storyline! It's brilliant.), Hellsing, Liar Game, One Piece, and Osamu Tezuka stuff like Adolf and Buddha.
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