I remember that it took a little while before I really noticed that the Ring didn't affect Tom, and when I realised it, I think perhaps it changed the book a little. The Ring was threathening the whole of Middle-Earth with its incredible power, but still it couldn't affect the mind of Tom Bombadil, what- or whoever he really is. It meant that the Ring could not manipulate everything, there was still hope. And though I don't know what Tom is (having read a few discussions about this here only served to make me more confused
), it is mentioned that he seems like something between a man and a hobbit in appearance, and his love for the nature around him, and many of his habits seem slightly hobbitish. If there was one person the Ring could not affect, perhaps there were others who could withstand its power, perhaps the hobbits would make it.
But the first time I read the book I didn't think about this, it takes a lot of time to notice the wonderful details of LotR, and I can't remember if I thought very much about Tom the first time I read about him except for "Oh, how odd. Why isn't he invisible?"