There are, to overgeneralize in a rather vicious way, two types of villains. There are the Awesome Villains—the complex ones who, whether completely insane or not, could've been something more and remind you of it every moment they're on screen/page. They are psychologically complicated and genuinely believe in what they're doing, even if they're still conflicted—somewhere. Then there are the DOOM Villains, who are evil...because...they are. They're ominous and scary and stuff, but not particularly fascinating in their own right.
But that's not necessarily a bad thing. Here's why.
It depends entirely on which relationships are important in the story. If the relationship between hero and villain is most important, you will (nine times out of ten, I think) have one of the Awesome Villains. If the relationship between the hero and some other facet of the story, whether it's another hero or the environment or whatever, then you're more likely to have a DOOM villain.
I KNOW. Let's have some examples! I love examples.
Let's turn to Thor. Loki is many things, but straightforward and uninteresting are not among them. He's a very uncertain, conflicted character, and his relationship to his brother is also the most important one of the movie.
If you turn to Avengers, you find that while he's still the antagonist, the amount of time given over to his complex and unstable psyche is vastly diminished, sending him inching closer and closer to the DOOM villain (IMO, anyway). This is, in my opinion, because the importance of the relationships has shifted—instead of being between brothers, the relationship has to focus on the Avengers themselves, being no less volatile than the previously attested fraternal relationship.
Similarly, while Captain America was a very good movie in many respects, the Red Skull is not especially compelling all by his lonesome. He's insane, yep, but he doesn't really have anything behind his insanity. But—for the most part—though it still irks me—that's all right, because the relationships focus on Steve Rogers & Peggy/Bucky/etc. The emotional core does not depend on the villain, as it does in Thor.
Oh, and then there's Doctor Who. *faints* DEAR HEAVENS, SO MANY EXAMPLES OF EVERYTHING.
Even their DOOM villains tend to be beautifully characterized, and the Doctor himself likes to take a nice stroll along Villain Crosswalk at times, so the categories get a little lumpy. Any time the Master shows up, though, you know an Awesome Villain period is going to pop up for the Tenth Doctor, because of their backstory as schoolmates and, y'know, only Time Lords left. That would be enough on its own, but further, Ten and the Master are virtually mirror images of each other—they have the potential to become the other, which is scary enough for Ten, but also rather curious in its implications for a drumbeat-less-Master.
Then, a regeneration down the line, River Song has her brief, timey-wimey episode of Villainousness. No further explanation is needed.
So Doctor Who doesn't really count, because it's always about the relationship between a person to good and evil. It's there in the abstract moments when faced with a DOOM villain (whenever the Doctor has to decide what to do with Really Bad People, i.e. Lumic) and it's there in the concrete moments when that relationship is given an absolute emotional core in the conflict between two people.
So. This is my Theory of Villains. Totally subjective, of course, but I like villains. I find them fascinating. Even when they are nightmare fuel.
*Although it's worth noting that the Weeping Angels are not really villains. They are antagonists, but villains by their nature must be individuals—possibly individuals linked to one another via an organization, but really there's only one villain.