You can get 500 AA miles for free by playing the Disney Planes game.

Link

Basically, all you do is fly your character around and collect symbols. Once you hit 3 or 4, you'll get the 500 miles and also a chance to win a trip around the world (380,000 miles). I'm not sure if there's a way to just end the game once you have 3 or 4, but I just collected all 24 like they asked. And once the game's over, you can enter your information to get the miles.


EDIT: Looks like it's only a chance for 500 miles. But in any case, it only takes 10 seconds, so there's no harm in trying!