[Farael]

I always thought Bombadil to be not unlike Melian, an Ainur who fell in love with Middle Earth and did not go to Valinor. That would explain more than a couple of things

*Why he did not disapear when he put the ring on (I'm assuming that Sauron didn't disapear either, it might be that if you were strong enough you'd be able to use the ring without disapearing)
*This whole Treebeard-Bombadil being the eldest (Ainur obviously don't count, or else as I said before, Olorin (aka Gandalf) would be older than Treebeard)
*His singing (As mentioned before, Arda was created by the song of the Ainur (and Eru) and it seems that Tom works magic by singing)

I can't recall right now if Gandalf says something about the nature of Tom Bombadil, but I think he could be a Maiar... I'd say even a Valar but I think they're all accounted for... and yet, he could be a Valar incarnated in a human (or humanoid) body like Gandalf. I don't know if it says anywhere that all the Valar were in Valinor during the War of the Ring.

In any case, I think that belongs to another thread.... but the point is, I think what Gandalf meant is that Fangorn was the oldest non-Ainur living thing.... as the Ainur are not alive in the same sense the elves, men or hobbits are.