Well, I like when the protagonist is the antagonist and the villain at the same time. The best character of all times according to me is Satan in "Paradise Lost", by John Milton.
He is most definitely after vengeance, he desires to hurt and destroy everything God loves. But at the same time, he is broken, abandoned, betrayed, hurt. His Father asked him pretty much to give up his bedroom to his cousin who just came to live with them and who gets all the favor (that cousin would be us, humans).
And he is ready to wreck that cousin's life from then on, even if it costs him his Father's love.
He is sly, conniving, sad, desperate and sensual. He will do anything to get back at them. He is the protagonist, he is the antagonist, he is the hero and the villain of the story. It is so magnificent I want to cry.