So, this is kind of interesting question for me because I don't like villains. They do their job and then they leave. (or DIE). I do, however, LOVE villains who aren't actually villains. Characters who appear as villains at first, but as you read you realize they're just MISUNDERSTOOD.
Case #1: Severus Snape from the Harry Potter series
Case #'s 2 and 3: Marisa Coulter and Lord Asriel from His Dark Materials
So, Marisa Coulter is bad because she's got an evil golden monkey daemon (which represents the soul and everyone knows golden monkeys are EVIL). Oh, she also steals children away from their parents and CUTS THEIR SOULS AWAY FROM THEIR BODIES.
Lord Asriel is bad because he wants to end God.
Okay, why they're amazing villains/not really villains: They looove one another. And they love Lyra. And I love them for loving Lyra because Lyra (the heroine of the novels) is AMAZING. They'd do anything for her and once you see them as a "father" and a "mother" you can't see them as hardcore villains anymore.
Have you a favorite villain???