I think Merida is the strongest, she fights for her own life and wins. She is not a damsel in distress at all.
I like Rapunzel as well, but she is not so stronger as others; Cindy is stronger... but we are talking about the strength of her heart, so she is keeping on dreaming after all.
I don't know why Ariel is ever the first, maybe 'cause she is the favorite out there, but I think she is just a selfish kid and she's silly sometime in the movie. Not like her at all.

I agree with you Lisa I loooove Merida too, the thing about Ariel I think is that she was the first; she faught because "she wanted to see the world her own way" even against her own father, and for a spoiled girl, takes a lot. She opened the door.

I think Cinderella is emotionally strong. She is forced to work as a servant in her own home but she still keeps a smile on her face and still has hope that some day it will all work out in the end and that there is a light at the end of the dark tunnel. But I guess that's just my opinion.

Or Mulan.

Phisically and in spirit

I agree with Popcornfan.

So do I.

Definitely not Merida, because while I love her, the very fact of her not wanting to get married and wanting to ~fire arrows into the sunset doesn't make her strong in spirit (not to mention that she never showed any sort of exceptional physical strength beyond being skilled in archery or climbing a cliff which, yes, defines her as physically strong in some way, but not in a special unique way because Mulan could do the same and much more), it makes her a 16 years old teenager who is just not ready for a relationship. She never got to endure oppression or mistreatment from the side of the only people she had and that were supposed to take care of her like Cinderella or Rapunzel nor was she punished for her open mind and different worldview like Ariel. Mulan is the strongest in terms of physical strength, but just like Merida, she never got to face emotional abuse or deal with manipulation growing up with a pair of loving parents. Indeed, she was considered some sort of an intellectual outcast because a rare woman in ancient china could successfully outsmart men in chess games and because of her clumsiness, but she wasn't raised in isolation like Rapunzel being constantly put down and psychologically tormented by her mother figure nor was she an orphan with no one but an uncaring stepfamily who used her as a servant and slave for her entire life like Cinderella. Basically, I consider Cinderella and Rapunzel the strongest princesses.

Psychically strong = Pocahontas. Mentally strong = Cinderella.