Falkor is the name of the large white dragon that Bastian and Atrayu ride in the 80's film The Neverending Story (which is part of the Holy 80's Trinity including The Neverending Story, Labyrinth, and The Dark Crystal). Has the ability to fly and bring luck to whomever travels with him.
In the Movie:
Falkor looks like a large white dog and is what most people remember about the film. "Yeah, that movie with that flying dog-thing!"
In the Book:
Falkor is described as lion-like, similar to an Asian dragon.
Atrayu rode Falkor as quickly as he could away from The Nothing.