I just started playing the fiddle, and "Angelina Baker," in the Mudcat index, was one of the first tunes my teacher gave me. "Arkansas Traveller" is also widely available, and I have seen words for "Old Molly Hare" and "Ducks on the Pond" in a lot of children's folk songbooks.

In related topics, "The Jolly Beggarman" is another um ... interesting song about maidenhood and beggars. For women eager to even out the lyrics, I suggest "Maids, when you're young never wed an old man." Both of these are Irish, I thought, but might be from anywhere in the Isles, I suppose.