Serious song: "Circle of Steel" by Gordon Lightfoot.

Not-so-serious songs: "Zat You, Santa Claus?" by Louis Armstrong.
"Big Dead Bird" by Lou and Peter Berryman.
Also, The Arrogant Worms have a Christmas CD entitled "Christmas Turkey". My favorite from that is "OH GOD, I'M SANTA CLAUS" (guy dreams he's Santa, then wakes up to find that he's really the Easter Bunny).
The Bob Rivers comedy troupe has 2 Christmas collections (that I know of) that include parodies such as "We Wish You Weren't Living With Us".

Dare I say that I've written some myself? One is the Christmas story from Joseph's point of view (a lot of people find that song hard-hitting; some are offended by Joseph's language during the "anger" stage of his reaction to Mary's pregnancy); another song bemoans the difficulties encountered by a Protestant woman celebrating the holidays with her Jewish boyfriend. Got 4 more songs besides.

SharonA