Well, I'm not much of a person to judge on comic book villains, but I'd say the joker. A crucial part of stopping a criminal (especially to a detective, which is what batman is, effectively) is finding out the motive, but what is the villain has no motive beyond causing chaos?
Done wrong, it could be a case of a one dimensional "evil for the sake of evil" villain, but the joker has enough mystery behind him and a genuinely interesting personality to pull it off. You believe he's utterly insane, you believe that he simply enjoys chaos, that he believes, to a certain extent, that it's how things are meant to be.
Favourite game villains are a little more difficult...because there's so many. Ranging from the utter joyous sillyness of Albert Wesker, to the believable creepiness of Sander Cohen, there's so many to choose from.
For sake of argument, I'm going to say it's Mr scratch from Alan Wake's American Nightmare, because, my god, more people need to know about Mr scratch. American Nightmare was a wierd game. It was a follow up to a strongly narrative based game that went for action, and for the most part, made it work. I've spent far more time on American Nightmare on the excellent arcade mode, but if anything made me care about the fairly short campaign, it's the villain, Mr scratch. He's a psycho who LOVES what he does. He's taken Alan's prescence in the real world, and he knows he's too powerful for anyone who doesn't already know about the dark prescence to stop him, and at the moment, that's pretty much just Alan. He goes around doing whatever the hell he likes, because nobody can stop him. It makes him a fun villain, and very accurate as the dark side of alan. He indulges in anything, and everything, no matter who it hurts. Ikka Villi, the model and actor for Alan Wake, also plays Mr scratch, and he does a great job of it, enjoying every moment.
And he has a kick-ass theme song
