An awesome question with so many answers. The great thing about villains is that it's so much easier to make a good villain than a good hero. To be a good hero, the reader has to actually like the character. Not true with a great villain.
Of course, some of the best villains are extremely likeable. This can be for a variety of reasons:
1: They are not actually evil. They are doing whatever evil stuff they do because they personally believe it's right and take no pleasure from their actions at all.
2: They are not completely evil. While they're far from a saint, they do have a nice side, maybe a soft spot for one particular person or perhaps they're extremely loyal to their family or have a habit of rescuing kittens from trees in their spare time.
3: They're motivated by a tragic past. Make it a really, really tragic past. Murdered, absent or abusive parents is usually a safe place to go.
4: They have one quality that makes them awesome! This can be being extremely cunning, witty or just downright hilarious. Honestly, if the character's genuinely funny, you can make them as evil as you want and they'll still be likeable.
But again, the character doesn't have to be likeable to be a "good villain." You know who I consider one of the greatest villains of all time? Joffrey Baratheon! You know why? Because you couldn't make him more hateable if you tried. I mean seriously, try to think of a bad guy you hated more than Joffrey. Evil masterminds who want to destroy the world for no reason are a dime a dozen and we're bored by them, but Joffrey is like a perfect mix of every detestable trait you can find in a person, all mixed together to create the most hateable character of all time. I consider him one of the greatest fictional characters ever because he does exactly what he's supposed to do. He makes you hate him. This is a character that's so fucking hateable that the kid that played him had to give up acting because of all the hate he was getting for his portrayal of his character (poor kid.)
So I guess to sum up, there are many things that can make a good villain, but the absolute worst thing a villain can be is boring. "I'm doing evil stuff because I'm evil." Is not a character anybody wants to see. The character needs a very clear personality (even if it's a really horrible personality) and he needs some kind of motivation for why he does what he does.