My favorites are as follows:
The Chessmaster / Magnificent bastard: Yeah, he's a villain, but he knows what he's doing. He's not there for comedy, he's not there just for the hero to beat up. He knows how to pull everyone's strings, he knows how to work the system, he's always one step ahead of the good guy, he knows how to exploit your weaknesses, and he's just a smug son of a bitch, but even if you hate him, you really can't help admiring just how incredibly good he is at being so bad.
The antagonist protagonist: For video games, this is the villain I get to control, the time when I get to be the bad guy, and the change of perspective is a lot of fun. Of course, for movies and TV, this is the series that shows everything from the bad guy's point of view, usually proving that he's not so evil or not so insane after all--if only in his own mind.
Sympathetic villain: This is often the villain that could've been a hero, would've been a good person, or maybe even should've been, but something went wrong. Life screwed him over, he lost someone he loved and snapped under the weight of grief ... whatever the reason, it's the villain you identify with, the one you learn to care about.
The Noble Demon: Not really a full-on villain, this one, closer to an anti-hero. He's a guy with a moral code of his own. He doesn't play by a hero's rules, he doesn't follow society's standards, he does bad things and isn't a good guy or a good role model for anyone ... but he has standards. He has a conscience. He has a sense of honor, duty, even compassion when it comes down to it. In fact, he sometimes has a heart of gold, buried way, way, freaking way down in there.