Mulan. She's the only "princess" with something to PROVE, not something to want. Even then her journey isn't inspired by something self interested but rather something sacrificial: she joins the army to spare her father from the ravages of war. She gains a sense of identity by the end of the movie, yeah, but that wasn't her motivation: that's just a bit of ancillary poetry, an emotionally nourishing cherry on top of the story. It's not the main focus, which is saving China from Shun-yu (or however you spell his name). Frankly, she's the only fully literate princess, and she's not even a princess.

 I don't like Merida or Rapunzel as stories. As personalities--that have been badly written for--I like them; but their stories don't become their intended characters. Which is a damn shame, because I really wanted to like their stories. Merida's especially.