DD is 5 and has seen some of them, but isn't gaga over them. Of the ones she has seen, she's seen them maybe once or twice, but doesn't ask to watch them over and over, and doesn't ask for tons of princess stuff either. She recognizes all of them, she got their pics and autographs at Disneyland when we were there this past spring, but doesn't care about watching the movies and stuff so much. She does LOVE Ariel (which I think is more about liking mermaids rather than princesses) but won't really watch the movie because the sea witch scares her. In most of them, there is something that scares her that keeps her from wanting to watch them. We took her to see Brave and she really liked it. She also liked Tangled.
DD seems to be that nice balance of girly-girl and tom-boy, so that while she does find some things princessy appealing, it isn't so much a part of her identity. She would rather draw and color and read and write then get caught up in playing princess, or dress-up, or mommy, or whatever. She wants to be a teacher when she grows up. I am not that much of a girly-girl myself so the whole princess thing is something I've neither encouraged nor discouraged. DD went to a princess-themed birthday party recently for a friend, that was held at a salon, where every girl got a princess make-over, with their hair put in an up-do, some glittery make-up, and a visit from Cinderella. DD loved it and loved how she looked. Then the next day she was fine with it being all over, the hair back to normal, the make-up all gone, and going outside to play soccer. :)
Coincidentally, we are taking her to see the Disney on Ice show featuring some of the Disney princesses. She'll probably like it more for the ice skating than the princesses.