Skin and Bones

My students love to sing this at Halloween and act out the part of the old woman, the bones, and the BOO!
Source: Locke, Eleanor G.  Sail Away: 155 American Folk Songs to Sing, Read, and Play. p. 52
As sung by Jean Ritchie of Viper, Kentucky

Phoebe

I love this song paired with a partner song composed by Denise Bacon.  The soaring octave jump in the partner song would be great for those vocalists who love to sing high and show off a beautiful voice.  It would also sound great played on instruments.
Source: Bacon, Denise.  46 Two-Part American Folk Songs

Old Mister Rabbit

This song could be used for vocal improvisation in thinking up other foods that Old Mister Rabbit could eat.
Source: Ed. by Erdei, Peter.  150 American Folk Songs to Sing, Read, and Play p. 11

My Paddle

This song sounds lovely when it's paired with a partner song, as Denise Bacon does, or sung in a round.  It's also great for presenting the syncopated eighth-quarter-eighth (or "syncopa") rhythm.
Source: Bacon, Denise.  46 Two-Part American Songs