I'm not real big on obviously-identifiable villains. Let's look at the anime Death Note for example since that series has had me hanging on the edge of my seat for weeks now. The two main characters are Light Yagami, who is a noble serial killer who has the idealistic goal of creating a new world without crime, and L the world's greatest detective, who isn't interested in justice, works with criminals, and wants to catch Light for the thrill of the chase and to prove that he is smarter than Light. Now, which of these characters is the villain? They both have strong reasons to like them and strong reasons to dislike them. (And me being a fangirl, I also value them because they have an intense ambiguous relationship with each other that it wouldn't take too much imagination to twist into sexual tension.)
Another example: Grima Wormtongue in The Lord of the Rings movies (and fanfiction) is definitely a villain, but a minor one not a major one. While in the books he's a pretty flat character, in the movies he was given the motivation of being madly in love with Eowyn the princess of Rohan, who shudders at the thought of him. Saruman promises to magically make Eowyn fall in love with Grima if Grima uses his position as advisor to subvert Rohan and prevent it from entering the war in opposition to Saruman. While Grima is obviously a villain in relation to the heros of the series, if you look at him only in relation to Eowyn the issue becomes less clear. Yeah he's basically a stalker, but he would never hurt her, he desperately wants her to love him and her disdain and disgust obviously hurts him. She doesn't take him seriously as a possible suitor or ever consider liking him in return, she just thinks he's icky and evil. He's educated, cultured, eloquent, subtle, mature, and amoral, in comparison to her being impatient, short-sighted, prejudiced, brawns-over-brain, and honorbound. It's easy to find an unrequited lover who gets a bit carried away to be a more sympathetic character than a narrow-minded stick-up-the-butt warrior, except in those few moments where she actually helps other people as a healer and a protector, and those moments when his superiority complex and ruthlessness show themselves.