Tink in Disney's Peter Pan gets stuck in the keyhole/drawer in the Darling house, but she saves herself.
Flynn and Rapunzel get stuck in a cave sealed off by rocks that is quickly being flooded with water in the latest movie Tangled.
In Brother Bear 2, Kenai the bear got his head stuck in a beaver's nest(whatever they call it) and Nita had to help him get his head out, which resulted in a lot of drama following.