Lord of the Rings Series -- Amazon

He's pretty much a complete non-sequitur to the actual plot (they meet a guy who the ring has no effect on, and indeed he exerts power over the ring by making it vanish and reappear, is known to be ancient even to the Elves, has complete control over his domain and likes to sing a lot, and then he's mentioned like one more time as a possible candidate for taking care of the ring but dismissed because he wouldn't care about the ring and would probably lose it), but he's undoubtedly an interesting piece to the world building of Middle Earth and has inspired a lot of debate and speculation over the decades.

The big question is to what/who was Tolkien alluding. Nearly everything in the book has a parallel to Catholicism or to WWII. My take has been that Tom Bombadil was a reference to Switzerland's actions (lack thereof) during WWII. A power that was strong enough to be immune to the Nazis, but without the interest to do anything about them. There is a certain nobility about him, and yet the Elves know they can't count on him for help.

If I have understood Tolkien's intentions correctly, I consider his character to be brilliant writing, but of course, there are many opinions about what he was supposed to represent.