Heh, what I think would be appropriate would be the guy asking you if he could ask your father to court you. It's your life, not your dad's. But asking the dad shows some respect. And that his intentions are honorable. I admit I would find that flattering and romantic, but I'm not sure I'd absolutely expect it.
I think guys should at least feel they should discuss MARRIAGE with the father, even if the girl doesn't live at home. Yes, it's mostly just a token of respect...but it's nice just the same.
Again, I'd rather he asked ME before my father. It would be kind of embarrassing to have my parents know before I did.