You guys all have great ideas, but here's my opinion on what makes a antagonist great.
Motivation is good, and madness is also good. But what I think actions can make the difference from a bad antagonist and a good antagonist.
Creative actions or eccentricities will make a bad guy seem a bit messed up in the head, which most villains are, and that makes them memorable.
Take for instance, the Joker from Batman: The Dark Knight. He just wants the world to burn, but he was perfectly fine. What made the Joker memorable were his behavior and his actions. This guy probably creeped a lot of folks out when this movie came out.
Another example: Sho Minamimoto. Sho was one of the antagonists from The World Ends With You. If you haven't played this game, (shame on you) Sho is a man with tattoos on his arms, and modern gangster style clothing. He's dressed to make old ladies run away from him.
This appearance might make you think of tons of archetypes, but he doesn't fall into any of them. This guy is obsessed with math, and makes junk piles in the middle of the road. He calls them "art". Math has made such an impact on Sho, that he talks about it constantly. He calls the heroes "Factoring Hectopascals", he references trigonometry, (SOH CAH TOA, or Some Old Horses Can Always Hear Their Owner Approaching) and he randomly says like 25 numbers from pi. Fans of the game quote him quite often, and he is a beloved character in the series.
Another one of my favorite antagonists is Baccano's Graham Specter. (Baccano! is an anime for those wondering.)
What makes Graham cool is that he carries around a huge monkey wrench, and he constantly contradicts himself. This guy seems pretty messed up. Just watch this, and you'll understand everything.
So therefore, an antagonist's worth, (at least a human one) is determined by his actions.