Others have held forth on this topic more expertly and extensively than I can, but here are some of my thoughts, such as they are.
One of the greatest things about him, is Bombadil will always be a mystery, as Tony has pointed out below. Tolkien thought that part of the richness of fantasy worlds lies in their depth. The Trilogy is scattered with references to earlier times, but it is never really explained until the Appendicies, but even that is sorely lacking. What this does for the reader is to put them into a world that they want to learn about; and, provide a way of doing that learning without spelling everything out. But mysteries always remain as they do in the real world. That is one of Bombadil's roles: the unexplainable element that provokes discussion and the desire to know more, creating a hunger that is ultimately insatiable. Therefore, the created world of Middle Earth has depth that cannot be measured, a cosmology that cannot be fully understood.
I'm sure there is a component of a family and their private jokes and mythology. Since much of this was written with his children in mind, I think he did it for them, or for himself.
Bombadil is one of my favorite characters, although I'm almost embarassed to admit it. He is the silliest character in the trilogy, but also the wisest. He can almost be viewed as a Taoist Sage in his way: he possess nothing therefore he owns everything. He does not strive with the forces of nature therefore they listen to his song. He speaks in riddles that go to the core of the understanding of self: "Tell me, who are you, alone, yourself and nameless?" As Goldberry said: "Tom Bombadil is the Master." * This would imply Valar (or more), but perhaps what Tom is Master of is himself. I'm not suggesting that Tolkien was envoking Lao Tsu, but this is how I have come to view Bombadil out of my own biased perspective.
Later, though, Tom declares (in one of my favorite lines): "I am no weather-master...nor is aught that goes on two legs." Yet he can wave the rain away and not get wet. Again, this is almost Taoist: Tom lets it rain, doesn't try to control it, but yet at the same time doesn't get wet when it does rain. He has no fear, therefore no need to control things outside his own getting wet in the rain. By this observation, he will not get involved in the Ring because it is not his way to control large events. Gandalf is another story: he is not supossed to met power with power, only inspire the residents of Middle Earth to realize their potential in removing evil.
Bombadil and Gandalf have a close friendship, almost like they understand each other in a way that no other characters can understand them, suggesting kinship or a common history or understanding. Remember what Gandalf said as he bid the hobbits farewell on the road from Bree to Buckland: "I am going to have a long talk with Bombadil: such a talk as I have not had in all my time. He is a moss-gatherer, and I have been a stone doomed to rolling. But my rolling days are ending, and now we shall have much to say to one another." Almost sounds like retirement, (which it is for Gandalf) and those two are going to spend their time playing golf on the Barrow Downs. This leads me to believe that Bombadil was almost a father figure to Gandalf, one he went to when his labors seemed fruitless or eternal - Bombadil is the only being in Middle Earth that can really understand him. (except for Radagast, but we don't know what his retirement was like)
Tolkien does use Bombadil to throw some heavy philosophy at the hobbits, but it kind of goes over their heads. Much of LOTR struggles with the ideas of free will verses fate, chance vs. determination. When Frodo asks if Bombadil heard his cries for help or if it was just chance that brought them together, in classic Tolkien fashion, Bombadil says both yes and no. "Did I hear you calling? Nay, I did not hear: I was busy singing. Just chance brought me then, if chance you call it. It was no plan of mine, although I was waiting for you." Bombadil seems to be describing a state of seredipity: he put himself into the situation in a way that increased the odds of them meeting, even though that was not his stated purpose.
Anyway, those are just some half developed thoughts on Bombadil, a very interesting character. Should Jackson have kept him in the film? No. He would have gone way over everyone's heads who thought him just a silly character. Who would have played him, anyway? Robin Williams?
~jms~
*lots o' easy jokes here: "master of his domain", or perhaps he is The Master, and his Tardis looks like a small cottage.
Off Topic » in reply to Ultimate nerd question: Was Tom Bombadil a vala?
He is.
