What good lessons do each princess teach?

Snow White: Don't eat food from strangers.
Cinderella: Accept help from friends.
Briar Rose: You'll never meet anyone if you never meet anyone.

Ariel: Don't just wait for your dreams to come true. Chase after your dreams, even if others tell you not to.
Belle: Don't settle for a man, and don't settle for him when you can make him better.
Jasmine: Always carry some pocket change.

Pocahontas: Give peace a chance.
Mulan: Give war a chance.

Tiana: Work hard to reach your goals, and don't depend on some man to reach them.
Rapunzel: As a young person, you have absolutely no idea how much free time you have on your hands with which you could be doing all sorts of incredibly creative and constructive things and learning all sorts of fun skills.

(Actually, for Mulan I'd say--Don't give up! But I just couldn't resist.)

Snow White: Listen to your parents and don't talk to strangers.

Cinderella: Accept help from friends. (I see that too.) And to never stop dreaming.

Briar Rose: You'll never meet anyone if you never meet anyone. (I see that too.)

Ariel: Don't just wait for your dreams to come true. Chase after your dreams, even if others tell you not to. (see that too.)

Belle: To accept someone for their beauty from within and not just by their appearance.

Jasmine: To accept someone for who they are and not by where they're from or how much money they have in their pocket.

Pocahontas: Give peace a chance. (see that too) And to accept people for who they are and not judge by their race and background.

Mulan: To believe in yourself and who you are. Because when you do you can make anything happen. Even win a war.

Tiana: Work hard to reach your goals, and don't depend on some man to reach them. (see that too.)

Rapunzel: As a young person, you have absolutely no idea how much free time you have on your hands with which you could be doing all sorts of incredibly creative and constructive things and learning all sorts of fun skills. (See that too) And to also set out to reach your dreams and not just sit around wishing and waiting for it. Make it happen by taking that first step.

All Ten from Oldest princess to newest:
Snow White: Don't talk to strangers
Cinderella: Always do good, be positive throughout life, and you'll be rewarded, (the lesson of rags to riches)
Aurora: True love exists, and always behave well
Belle: see a person by the personality, not the appearance.
Ariel: everyone makes mistakes, but in the end always do the right thing, don't let fear get to you.
Jasmine: Never change yourself just because of others.
Pocahontas: Be brave, make the right decision, and follow your heart to the truth.
Mulan: Women are just as great as men, knowledge and diligence give great rewards, don't be someone you are not for the wrong reasons (she used it for the right reasons)
Tiana: Never give up, don't wish for something MAKE IT HAPPEN (that's not my motto but it's my quote >.<)
Rapunzel: Do the right thing.
(Giselle doesn't count officially because she's not in the line up and because she a modern version of aurora and snow white...and maybe ariel O.O which also goes for alice, jane, megera, and melody.)

Snow White: Make the best out of a bad situation
Cinderella: Believe in your dreams
Aurora: Put your responsabilities ahead of you
Ariel: Follow your dreams
Belle: Don't judge by appearances
Jasmine: Forgive and forget
Pocahontas: Respect others no matter their skin color and how different they are from you
Mulan: Women can be just as good as men
Tiana: Work hard to fulfill your dreams
Rapunzel: Make sacrifices for your loved ones
Merida: Don't make harsh decisions