whew - this thread is making me a bit teary...
I think it just boils down to each person and her relationship with her dad/mom/parents. Personally, I told my (now) husband that I didn't want him to ask my dad for permission (the thought of that rubs my liberal, feminist, bra-waving heiney the wrong way), but I did want him to ask for my dad's blessing. I think of it more as an acknowledgment that I'm not a piece of property and I can do as I see fit, but that my dad (and mom) were saying by giving their blessing that they recognized the commitment my fiance (husband) and I were making and agreed to give support and guidance (when asked).