Hands down, the most pointless, irritating and twee character in the novel, and very deservedly left out of the movie.
The early chapters of The Fellowship of the Ring are something of a mish-mash, as though Tolkien couldn't decide which direction he was going, and when he did, didn't bother to come back and edit.
Tom Bombadil serves no narrative, thematic or other purpose. He's just a silly character who arrives in the nick of time to save the hobbits from relatively minor danger that is a sidebar to the narrative.
When I periodically re-read the novel, I skip the entire section from leaving the house at Crickhollow to the arrival at Bree.