Disney has taken on most of the famous European/American fairy tales that most children know - though do they know them from being told, or seeing the Disney movie we'll never know. From The Little Mermaid, Beauty and the Beast, Peter Pan, Snow White and the Seven Dwarves, Cinderella, Sleeping Beauty, etc. they've covered the genre quite well. Thankfully, they are actually timeless stories that can be retold and actually stand up to the retelling (though not all the time).
Here are my favorites (which is not to say they're good, but there are parts of them that I like because of some twist on the story