My campaign has plenty of enigmatic characters, but few as extravagant as Tom Bombadil. I think the closest character would be a traveling wizard who calls himself The Great Whamboozy. He travels from town to town, showing off his magic tricks, and often involving the audience (and coveniently the players) in his performance. The catch is, that his tricks are anything but innocent. A seemingly simple vanishing trick that he often performs, actually temporarily banishes his volunteer to another dimension, before bringing them back right around the time they start panicking. It is no surprise that he never performs in the same town twice.
He is the sort of character I throw into the campaign whenever I want some lighthearted fun that is totally unconnected to the rest of the plot.