I've noticed recently that there's been a sort of a flip on the traditional role of primary characters; we see heroes portrayed as the enemies of the main characters in fictional works. Mind you, this isn't to say that suddenly every work of literature is written from a villain's perspective, but there certainly is something to be said about it.
This takes multiple forms, too. For instance, we have the protagonist villain who earns his "villain" title more by his standards rather than his ideals. This sounds more complicated than it is. A great example of this is Doctor Horrible. He wishes to form a more perfect society and right all the wrongs that he sees, with his own power hunger being an extension of his desire to make the world a better place. He even balks at killing for the majority of the story (and never kills anyone even after he makes plans to). This is a villain protagonist only in the sense that he is a villain only by convention, his methods used and his ideals vary from those that are acceptable, but he has good intentions and is as such a sympathetic character.
Second, we have a character similar to Tom Clancy's John Clark, who does horrible things for the right reason. This sort of character is sometimes referred to as an "anti-hero", but I feel it is better to name him as a villain protagonist. The only reason John Clark is considered a hero is that he fights for the good guys and his motivations, much like Doctor Horrible, are to protect, though they are more self-serving. He entirely rejects society and tends to act in consideration of his own good and for people he knows rather than for a loftier goal, which is what sets him apart from Doctor Horrible. This second type of character is more willing to strain the rules and break them because he doesn't care about society. Figures like this tend to earn sympathy because they are very much like the average person but with less restraint or more violence.
The third common form of villain protagonist is the "damned" character, who has decided fatalistically that there is no way to be redeemed and he may as well do what he can now, but disregards ethics or benefits of his actions. A classical example of this would be Achilles, though a more modern example might include vampires of a more realistic perception (basically Vampire the Masquerade vampires). They often have a sympathetic element, but their connection is more one of pity than of empathy, and nobody would dispute that their actions are evil, though justifiable.
The final common form of villain protagonist is the monster. They are the sort of character with no redeeming value whatsoever; if they stop someone from burning down an orphanage it's only because they've already lit fires in a different wing of the building. They are, however, still enjoyable as characters for the psychological case study they provide, as well as the fact that their actions produce a feeling of schadenfreude or superiority in the audience, but they are not the sort of characters that one would see a particularly large following for.
The main form of heroic antagonist, however, is the petty hero. To use Doctor Horrible's Sing Along Blog as an example yet again, this would basically be Captain Hammer. For those not aware of the plot of the show, Captain Hammer is the over-the-top hero who works primarily for his own benefit; he often puts on a face of compassion, but his actions are mostly spurred by bullying Doctor Horrible or getting whatever he wants for himself (Fame, recognition, Doctor Horrible's love interest), rather than the benefit of society. This hero rarely exists without the presence of a villain, because if there is no villain they tend to be more towards the second type of villain protagonists, since their motive is societal gain for personal benefit.