One of the things that bugs me about a lot of the sci-fi/fantasy genre, which I'm otherwise so fond of, is the legend of the "Chosen One," the one person touched by the hand of fate who inherits the magical powers or the Royal Birthmark or whatnot, needed to save the world from whatever dark forces conspire against decency and goodness.
It's a common theme throughout a lot of modern popular entertainment, whether it be Superman, Harry Potter or Star Wars. If you're not that special someone, you don't even rate and are a Comic Sidekick at best or collateral damage at worst.
Unfortunately, for a lot of female characters get the worst of this, where not only do you have to have some special birthright to get the starring role, but you don't even get to kick butt, you have to sit around and wait to be rescued. Yep, you get to be a Princess. If you're just an ordinary girl, chances are... well, you probably won't even be mentioned in most stories. No magic powers, no daddy the king, nobody cares.
But there is a rarer type of hero, in contrast to the King Arthur model, there is the Brave Little Tailor, what author Charles de Lint refers to as the "Jack."
The Jack is a subset of the trickster legends, where, in lieu of super powers, a sword in a stone or a fairy godmother, the hero relies on intelligence, courage and sometimes more than a little luck. I like these stories better a lot of the time. They may not have the grand scale of the epic hero, but then again, there can be a bit too much of that sort of thing anyway (Wheel of Time, anyone?). If you have to save the world every Saturday, the thrill kind of wears off after a while, the constant escalation gets a bit annoying for the reader/viewer. The small adventures have a charm of their own, coupled with the feeling of "hey, that could be me!"
Of course, it's a bit tougher to find a female Jack (a Jill?) in the mainstream of the genre, but I think it's worth looking for them, especially speaking as the father of a young girl. You'll see some of them in the Urban Fantasy genre, where Authors like de Lint have taken delight in pitting Everywoman-type protagonists against all sorts of mystical beings, but that's still a fringe of a fringe. Hollywood, on the other hand, doesn't seem to have gotten past the idea that a female fantasy/scifi protagonist doesn't necessarily have to be a combination sharpshooter/ninja/acrobat/swimsuit model.
Princesses are fine in their place, but they are, by definition, an exception. Where do you point an ordinary girl to show her genre heroines she can identify with?