Iago from Shakespeare’s Othello, and King Claudius from Hamlet are both villains that make me seethe with rage. Denethor (from the LotR books–I haven’t watched the movies so I can’t speak to them) is an example of a “villain” whom I pity, yet despise.
Also Loki from the Marvel movies. He’s a villain at least some of the time, and I go from sympathizing with him a lot, to wanting to give him a good right hook, to cheering for him.
Don't cry for me, for I go where music is born ~J.S. Bach