I remember reading at one point that Bombadil represented something that was older than Sauron, older than anything in the memory of the world. That he was essentially nature embodied, and "little things" like the ring of power were so beneath him that it didn't even have a chance of affecting him.
I don't think he's Maiar, since all of the Maiar of the Third Age were restricted by certain covenants of action, and even Saruman couldn't/didn't act against some of those covenants. Bombadil seems much more powerful and primal than a maiar.