Here is a great online tool that teaches you how to play any song by ear. At the absolute least it’s a great introduction to music theory and how songs are built.
The principle at work when learning to read music and play songs is one of relation. How one note (or chord, or melodic line) relates to another. But some people can learn songs without any point of reference at all. Check out an introduction over at the Instant Guitarist blog entry: How To Learn Perfect Pitch. The post describes the concept of perfect pitch (also called absolute pitch) in a great way:
Perfect Pitch is being able to identify a musical note without a reference note. Basically, you can tell what any sound is in the world and classify it into the seven notes. Soon you will hear car horns, clanging cans, or even laughter as musical notes.
Perfect pitch, then, is the ability to hear the world as music. This makes it a worthwhile skill for musicians and non-musicians alike.
Check out the wikipedia article to learn more about this phenomenon, as well as the controversy surrounding the ability to learn it.