The French have a word, jolie laide, for “good-looking ugly women,” women such as Anjelica Huston, Bette Davis, and Tilda Swinton. There isn't such a term for good-lucking ugly men, but there should be, and one of the prime examples of that would be Girls (and future Star Wars) actor Adam Driver.
He's a really good actor—he has made his Girls character go from being a reprehensible, shirtless, sex-addicted slacker to being a caring, shirtless, sex-addicted slacker. In other words, the character has remained true to himself, even though our perceptions of him have changed dramatically through the seasons. That's due as much to Driver as it is to the show's writers.
He'll play the villain in the forthcoming Star Wars movie, and it'll be interesting to see what he does with a role that is likely to be less nuanced and bigger than his previous work (similar to another 'ugly-pretty' actor, Benedict Cumberbatch, who was the villain in Star Trek).
While Cumberbatch looks good in static pictures, Driver just...does not. His face, when at rest, is odd, and it's difficult to explain how appealing he is without seeing him in motion, a fact he recognizes:
I'm like a sight gag, I have this really big face...I don't totally get it. I mean, when I read for Girls I was, like, the script says 'Handsome Carpenter,' so someone else is going to get the part. They'll have someone handsome, not me. I mean, I'm not in any danger of getting leading-man parts.
But watch him in motion, and you can't take your eyes off him. There's this very poignant, lovely, disturbing scene where—even though they've broken up—Hannah calls Adam and he responds exactly as you'd want someone to, literally running (without bothering to put a shirt on) to her apartment.
“I was always here.”
And then there's his voice; he's got this low, strangled way of speaking that seems as if he is holding his emotions in, even though (at least on Girls) he is painfully honest, saying precisely what is on his mind. The way he calls Hannah “kid,” even though they're not that far apart in age is so sweet, and he only uses the epithet when he wants to reveal his feelings and caring. In real life, he doesn't speak quite as growly.
Then, to talk about the 6'3" elephant in the room, there's his body. A former Marine, Driver is ripped in a natural (albeit hot) way. He spends most of his time on Girls shirtless, and that's a good thing.
He has this presence that transcends the reality that he does, actually, have sort of an odd face. And more than presence, he is a good actor, and makes people want to watch what he does, which is probably why Stephen Spielberg, Martin Scorsese, and the Coen Brothers, among others, want to work with him.