In a recent talk with Famitsu, Aonuma confirms that Zelda is not a Princess in Skyward Sword.
Eiji Aonuma, producer of Legend of Zelda: Skyward Sword, discussed Zelda's role in the story of the game as not being that of a princess:
"She's not a princess this time which is something I'll pretty much have to put forth right now in order to talk about this title.” He then continues by saying that “She’s a childhood friend, but she goes away in the midst of the game and it's Link's job to search for her."
This makes sense when coupled with news that the game’s timeline will predate Ocarina of Time, leaving open the possibility that the story will somehow explain the origin of the Hyrulian Dynasty.
Aonuma also pointed out that this change will also affect how the games story plays out. "This game's plot is something like a school drama, you could say. The flying sequence at the E3 demo is Link competing against his classmates. One of them looks kind of a like a bad guy, as you saw, and he shows up in other ways in the game too, since he has a major thing for Zelda."