The Yin/Yang of a Beloved Villain Character?

Absolutely!

Raymond Reddington from "The Blacklist". If ever there was a kindly sociopath, (I know that is a contradiction in terms) Red is it!

David from Alien Covenant is great, because he doesn't want to be a robot. Also, Ray Marcus from Nocturnal Animals represents the need to separate the uniformity of reaction from the uniformity that ends bias

This guy.

I am absolutely in lust with him.

Mr Gilbert from The Inbetweeners.

Some movies have the villain start out being reprehensible, then works to make them sympathetic. I never did buy it. A perfect example is Glenn Ford in 3:10 to Yuma. He starts out robbing a stagecoach. He shoots through one of his own men to get the stage driver. By the end of the movie he heroically helps his captor fight off his own gang, which is just trying to free him, and rides off on the train to justice. Just doesn't make sense to me.

Awesome movie though, right? I kind of got the idea that the hero (villain) had an attack of conscience, just wanted to do one good thing, and once he started it was too late to stop. Maybe he thought of his own father as a failure, or a weak man and remembered how much that hurt, or realized that was what ruined his life. maybe he saw that it was too late for his own redemption but this boy had a chance if he could just look up to his father.
I don't know. Good movie though.

I think you can call Yuma a redemption flick. No matter how twisted the evil doer is, there is a flicker of goodness deep down in all that cess pool that will respond in a noble way. I agree with you Edgar, it doesn't make any sense.