Just last night, I started reading The Arabian Nights to the kids at bedtime; my wife bought it to inoculate them in advance of seeing Disney's Aladdin someday.
Which, anyway, is kind of blowing my mind right now, because some anonymous commenter somewhere a couple of years ago argues that it's set in the future, specifically, "a post-apocalyptic world" at least 8,000 years from now, "where only Arab culture and some Greek survived," and where "amazing technological marvels left behind by the previous civilization, like sentient flying carpets or genetically engineered parrots which comprehend human speech instead of just mimic it are taken for granted by the locals or considered 'magic'."
Which would be crazy enough, if six minutes later, some other anonymous sage hadn't revealed that "Disney Princesses are like the Eternal Champion, all the same person born in different times and places."
I mean, holy crap, it's like A.I., Twelve Monkeys, Kundun and that one ST:TNG episode, all in one! It also explains why the princesses never make eye contact with each other: that's the only way to keep the wormholes in the fabric of space-time from collapsing in on themselves and obliterating this entire instantiation of the multiverse! How could we all have been so blind??
UPDATE Though this future theory is entirely dependent on there being "no way for [the Genie] to know of the fashion trends which have happened" in the 10,000 years since he's been trapped in the lamp. So the whole thing falls apart if if he had like, Tumblr, or a subscription to Vogue or whatever.