The basic truth to any hero is that he's only as good as his villain. And as such, he bears some serious consideration. There are basically three kinds of villains: Failed love interests, Arch-rivals, and Elementals. Let's explore!
Arch-rivals are the meat of the relationship. The hero needs someone who is capable of testing him, and is going to make the challenge seem interesting. Sometimes the rivalry goes way back; Dr. Doom has been challenging Reed all the way back to their college days. Other times, it goes to when they first clashed; Lex Luthor wants to slam Superman because Superman sent him to jail when they first met. And then there are those that simply represent different perspectives; Ra's Al-Ghul is Batman done Evil.
However, the basics of the arch-rival will always be the same: The villain needs to challenge the hero, and a have a reason for the grudge. The challenge is the fun part, and it doesn't mean that the villain has to have the same powerset as the hero, or even have a powerset; Lex Luthor has done rather well, and he usually doesn't even have a powersuit. Luthor challenges Superman by threatening his ethics; Luthor is a womanizing, plotting, unrepentant bastard, and proud of it; he has fun doing what he does, and he's pretty good at it. But...he represents a threat that the Blue Boy Scout can't handle easily; he can't physically attack Lex, and Lex is a far more complex problem because he is part of the power structure of Metropolis. Lex has always been a fun villain; he's evil, he knows it, and he's always steps ahead of Superman.
And the grudge is just as important. No matter how multi-dimensional your villain is, if he doesn't have a grudge against your hero, then the villain just doesn't work. When you think grudge, screw the logical side of your brain; apply the angry side of your personality. And I'm not talking merely being anti-authority; I'm talking the villain has been arrested or humiliated by the hero, or thinks that he has been. Dr. Doom has gotten a lot of mileage out of Reed embarrassing him back in college, when Reed tried to point out his math error; he's seen every defeat since then as further humiliation. Batman slighted Ra's Al-Ghul by not marrying his daughter and wanting to take over his organization.
And, even though I'm using a super-villains, this doesn't apply solely to them. It can apply to high school (the Supreme Jock and Ultimate Popular Girl are the obvious cliches), the office (the backstabbing secretary and the sadistic boss), There is almost no limit to where you can find the arch-rival!
The Failed Love Interest can be downright fun. Besides revealing part of the hero's psyche (what kind of woman the hero likes can reveal a lot), it creates an interesting character that can sometimes annoy, sometimes support the hero. The FLI can be anything, from a stalker, a radical (getting into trouble by proving how good he is, for example), ethical rival (loves the hero, loves stealing more), or even obligation (needs to marry the hero in order to fulfill some personal quest). Anything that applies to the normal love interest applies to the failed one; after all, the FLI could have been the love interest except for some “tragic”mishap. Except, of course, that the FLI is just a bit twisted; she may be out to kill the hero, humiliate him, or even just be doing what she is doing in order to get the hero's attention. And, even more evil, she may team-up with the hero in order to save him; nothing ends a romance like the death of the romanced.
A special note on this one: One of two situations can really mess up the situation. The first is that the hero could represent the one way in which the villain is a potentially good person. This is great for tragic storylines, or when you just want to make the villain a bit sympathetic. It can even be used if you eventually wish to redeem the villain, and this is usually the first sign of that.
The other is much nastier. In essence, it's a version of the Arch-Rival, but nastier; the FLI is trying to prove herself, and the easiest way to do is to be the center of his universe, which is naturally enough his arch-rival. Or, the “failed” part could be humiliating to the villain, and forms the basis of her grudge. This can get really tragic...
The Elemental is something that is intrinsic to super-hero and fantasy comics. It requires a focus of mind that just doesn't work in other genres. I'm not referring to characters made of some elemental force; I'm referring to characters that represent some aspect of the universe. Consider The Joker for a sec: He represents the evil, insane, twisted part of the human psyche. He and Batman clash more because they represent opposing forces (Sanity versus Insanity) more than any mere rivalry. By representing some aspect of the Dark Side of the Universe, the Elemental allows you to play with the fundamental forces that make up your universe, and show that it can fight back on its own terms.
Sort of makes The Joker scarier, doesn't it?
By using these three kinds of villains, you do something weird: You give the hero something to do. You give him a chance to show why he's a hero, why he fights, and what he's willing to do to win. If you look at the support staff as providing the reason for why the hero does all of that, then the villain is ironically the best support a hero could ever have. Keep that in mind, and you will do really well!