The Coventry Carol is properly a Christmas carol, but it recounts an episode we usually leave out of the story. The Massacre of the Innocents is the dystopian flip side of the Epiphany.
Lullay, My Liking is one of my favorites. A medieval text, in a setting by Holst, it's not often recorded, but worth looking for.
Jesus, Jesus, Rest Your Head is an Appalachian carol, contrasting Jesus' innocence with 'all the evil folk on earth', while another American song goes right to the heart of the matter: for Poor Little Jesus there will be no place to rest his head.