The self-rescuing princess is the ideal princess that doesn't wait for a guy to save her. That's easy.
Tiana! Is awesome. Tiana works hard, saves her money, and starts her own business. Her Prince Naveen is lazy, happy, and broke. He gets Tiana in trouble in the first place, so any rescuing he does, he owes her. :) The best part about Tiana and Naveen is they each learn something from the other. She learns how to have fun, he decides to do something with his life besides party.
Cinderella gets a few self-rescuing points for keeping her spirits up and winning over the prince with her personality. Her fairy godmother helped her get to the ball by providing a gown and transportation; Cinderella did the rest of the things she wanted--mainly, go to the ball and have fun. Face it, her story really is about an amazing thing happening to a random girl. Sometimes life is like that.
Belle rescues her father. He thinks she needs to be rescued. Her friends rescue her from Gaston. She rescues the Beast from the spell. Beast rescues her from a lifetime of boredom in the Village that Wouldn't Read*. There is ALL KINDS of rescuing going on here!!
*"Reading Rainbow" was the least popular PBS show in Belle's village.
All right--She-Ra! She always self-rescues, right? Yeah, only after growing up evil, thinking the Horde was the opposite of evil, cruel, and unjust. Her brother and the Sorceress of Grayskull rescue her and then she rescues her brother...and pretty much everyone else for a couple seasons of fine 80's television.
Rapunzel knows how to knit, throw her voice, play guitar, paint, make candles, bake, sew, and use a frying pan as a weapon. She rescues Flynn from the palace guards, Flynn rescues her from herself, and she saves Flynn's life with the last drop of golden flower magic. Rapunzel, Flynn, and Maximus make a great team, along with the thugs at the Fuzzy Duckling. This movie was so HackMaster...
While I fully support the self-rescuing princess--the one who takes steps to change her situation or save herself, I wonder if its healthy to expect someone to do everything all alone. We have friends and families, churches, clubs, and teams for a reason. We help, coach, and back each other up. A HackMaster adventuring party is made up of a variety of characters with different skills banded together to survive in a dangerous world. Is it fair to expect the princess--or the girl character--to be fully self-sufficient, rely on no one, and come up with the perfect solution to every problem every time? Is that even realistic? She should get a hero's journey of her own, no question, but the hero only goes it alone for part of the story. For most of it, the hero has help or companionship--something worth fighting for.
If you want to go it alone with everything, fine. I read a great interview once with a lady whose husband gave her crystal meth to help her be the bestest, do-it-all, working mom, housekeeper, and little wifey ever. It worked until that pesky addiction kicked in and she ended up in prison. Also, it turns out crystal meth is an illegal drug made out of stuff like nail polish remover, not fairy spells and sunbeams.
I don't think characters should always self-rescue. I do think they should try. My current HackMaster PC, Gabriella, happens to be a princess. (I randomly determined her social class.) She is banished from her home and out adventuring because she has to make her own way in the world. She doesn't wait for the rest of the party to get her out of a jam--she contributes her own sword and shield. I'm pretty sure my GM and fellow players would kill me (the GM literally) if I declared Gabbi's action to be: "I run around screaming and try to hide behind the magic user! Aaaaahhh, that orc messed up my hair! Save me, save me!" There is a big difference between THAT stereotype and a princess doing her best to survive in the circumstances presented to her.
Also, Belle and Tiana fell in love with a beast and a frog, respectively. Kinda weird, girls.
And now to self-rescue from this fever. Good times...