I voted for “Father Christmas” but since I don’t actually celebrate Christmas—I celebrate Atheist Kids Get Presents Day, which coincidentally is also December 25th—here’s my favorite non-denomential holiday song.
You probably have never heard of Bob Czina. He was an early computer-assisted musician/composer. During the dot-com boom, I had a syndicated computer talk show that, one year, hit on Christmas Day. Not wanting to talk, I contacted the Computer Music Association and they put me in touch with Bob to see if he had any Christmas music. He told me he had been working on a suite called “Child of the Christmas Heart” and he would see if he could get it done in time for the show. He did, it aired, and was beautiful and filled with warmth and joy. I did not know that Bob was in the final stages of brain cancer. He died a month after the broadcast. His widow told me that getting this final Christmas “gift” done helped him keep going. I still get to use parts of it each Christmas on another show, and hope to have it on my site, sillycatvalley.
Sufjan Stevens has several good Christmas songs, but my favorite off-mainstream one is The Boy Least Likely To with their Christmas/Wham! mashup of “George and Andrew”. It’s the fantasy you never knew you had; a Christmas Eve reunion where a washed-up Andrew and glistening George run into each other in a London bar.
And while Eartha Kitt has the standard, Kylie Minogue knocked “Santa Baby” out of the park with her vamping (sorry; all I could find was a live version.)