[Suzerain of Sheol]

As far as I know, there's no consensus on just what he is. Tolkien said in a letter that he's a secret and going to stay that way. One of the things that makes the world seem bigger, you know TB is going to be there after the story ends, and he'll be just as mysterious then as he was early on. Life goes on.

I can't remember if he recounted Beren and Luthien or not. It was either him, or Strider at some point on their journey.

My personal pet theory is that Bombadil is a Maiar from the court of Yavanna who came into Arda as it was being sung into existence, before Morgoth touched down to earth and infected it with his evil. He seems to represent Arda unmarred, and if he was a Maiar on the same order of Sauron, it would explain his ambivalence toward the Ring.