In this new Zelda game it seems like Zelda's just Link's friend, not a princess. Take a look at this:

The Legend Of Zelda: Skyward Sword Video Game, E3 2011: Story Interview (Stream) | Video Clip | Game Trailers & Videos | GameTrailers.com

When he catches the statue, he says "Wait till Zelda sees this!"

And in the trailer when Zelda gets zomg eaten by a whale, she definitely doesn't look like a Princess. And since this game apparently explores the origins of the Master Sword, maybe it'll explore Hyrule's history too.

And I like how some interviews are saying it'll be structured like a Metroidvania, too.