I'm not so insecure about my relationship that I feel the urge to fight off any guy who comes near my girlfriend. I'm pretty sure she wouldn't be even remotely interested in some drunktard at a bar, so there's no need to show off what an alpha male / tough guy I am and that she's lucky to have me or whatnot. In fact, I think my girlfriend wouldn't like it at all if I punched anyone anyway.
That said, if he keeps being annoying to both of us I suppose I'd politely ask him to fuck off or otherwise ask his pals to keep him on a leash.
I just really don't see what good punching the guy in the face will do. At best the guy just walks away, but in a worse case scenario you have his buddies all over your ass and get yourself a few punches in the face back.