1. Magic. There has to be magic somewhere but it is not the be all and end all in a fairytale either. See below. Also it is usually acknowledged there are limits to what magic can do.
2. Characters have to make choices. This is generally true of all fiction but in fairytales, the characters still have to decide something has to change. Cinderella wanted to escape her horrible life but still needed to be willing to do what the fairy godmother told her. (Couldn't you just see the ugly sisters arguing with the godmother? I could!).
3. An appropriate ending. Most of the time in fairytales this is the traditional happy one, but not always, as Hans Christen Andersen proved with The Little Mermaid amongst others. Having said that, his ending to that story was apt for the way he'd written all that came before.
4. There has to be some hope. There has to be hope for the characters to achieve their happy ever after ending or, if they know this is not going to be the case, what can they salvage to make things as good as they can be? If you have to settle for second best, you are still going to want that second best to be as good as possible.
There are other elements of course but these strike me as being amongst the most important ones. Comments welcome!