Back in the day, it wasn't a question as to whether or not a guy would propose—it was a question of when he would do it. Times were different than they are today. Young women lived with their parents until they married, and that was standard from the beginning of time until about 50 years ago. Now, if they can afford it, most women get their own apartments when they graduate from school, whether it's high school or college. They have bank accounts, jobs, and independence. Even if they move out a bit later, many modern couples end up living together before marriage. Which makes the whole "ask for permission" thing seem equal parts old-fashioned and silly.
But then there's the matter of tradition, and no event honors and nurtures tradition more than a wedding. There's the walking down the aisle, the I dos, the first dance, the toasts, and countless other rituals that make a wedding a time-honored experience. Before any of those things can happen, though, there's got to be a decision to marry, and for many couples, the first question asked isn't, "Will you marry me?" but "May I marry your daughter?"
Asking her dad for his permission is meant to show respect but it's now perceived by some as sexist. Why ask the bride's dad or both parents for permission? She isn't property that's meant to be traded, as women were in the past. And how come the bride doesn't have a similar question for the groom's parents? While it would be hard to believe anyone involved in this Q&A takes it as a serious request, it's something to think about. In no way should a man talk about marrying his girlfriend with her parents before he's discussed it with her first. Big life decisions should be talked about thoroughly and repeatedly before anyone hops a plane to the bride's parents' hometown or a ring is bought.
Like many things related to weddings, asking her parents for their permission is a long-held tradition, but it may not be right for everyone. As long as the bride and groom discuss whether or not to do it beforehand, they're good to go. If you think her dad would appreciate the gesture, then do it as a formality. If you know your girlfriend would hate the idea, skip it. And if the idea of asking for "permission" at all feels like too much to swallow (you are both adults, after all), then try asking for their blessing instead. That way, you're making it clear that you intend to propose, but that it would mean a great deal to you to have their support first.