Doesn’t have to be sung in a church to be a carol.
“Last Christmas” by Wham! I’d love to see a group of carolers go around singing that one!
Definitely.
There’s also Martin Mull’s “Santa Doesn’t Cop Out on Dope” from around 1975.
Heh, touche, Monte. Okay, so now all I got is Jingle Bell Rock. Don’t throw any rocks at me, you all know that you like that song now! 
I tried to find out when “Carol of the Bells” was written, but couldn’t find much; it does appear to be from an old melody. It’s one of my favorites. To me, Christmas carols will always be associated with church, but that’s because of my upbringing - my father is clergy (Episcopal priest) and my mother was a church organist (many carols this time of year make me think of my Mom too–so it’s good, but also makes me feel sad).
Just remembered: Paul McCartney’s “Wonderful Christmas Time.”
No kidding?! Did he (or you) know Dr. Harper of St. John’s in DC? I was an acolyte (back in my Episcopalian days) when he was Rector.
Sorry, Monty! Even though I live in the DC area, I didn’t grow up here–my Dad served in Delaware and PA (Philly area). He actually started out as a Baptist minister, then went to the Congregational church (those churches were in MI), then finally became an Episcopal priest in 1965.
Another good thread for plugging the Carols for a Cure Xmas CDS. Broadway Cares/Equity Fights AIDS has released one a year since 1999, and they combine the old and the new. How can you not love the Full Monty doing “A Full Frontal Christmas”:
By the chimney hung with care are my stockings and underwear
It’s gonna be a full frontal Christmas this year.
There’s nothing stirring in the house. Where is Santa? Where’s my blouse?
I’m hoping for a full frontal Christmas this year.
Well hello man, take the coat off that snowman for Frosty’s beginning to thaw.
He’ll grin and bare it. Look at his carrot. Sing it: Fa La La La La La La.
I’m a huge fan of modern Christmas songs. 
In addition to the Wham!, Paul McCartney, and The Waitresses tunes mentioned above, here are my favorites from my iPod:
Run DMC – Christmas in Hollis
The Kinks – Father Christmas
Elton John – Step Into Christmas
Billy Squier – Christmas Is The Time to Say I Love You
The Royal Guardsmen – Snoopy’s Christmas
Karen Carpenter – Merry Christmas Darling
Sting – Gabriel’s Message
Gary Glitter – Another Rock and Roll Christmas
The Beach Boys – The Man With All The Toys
The Beach Boys – Santa’s Beard
The Beach Boys – Little Saint Nick
Wizzard – I Wish It Could be Christmas Every Day
Stevie Wonder – What Christmas Means to Me
Stevie Wonder – Someday at Christmas
Band Aid – Do They Know It’s Christmas
Emerson, Lake, & Palmer – I Believe In Father Christmas
Blink 182 – I Won’t Be Home For Christmas
I’ve seen that. Well, it was a staged group of carolers on a Japanese tv show, but it did look cool. Plus, I like the song.
Annie-Xmas: Those lyrics look like they belong on the Twisted Tunes collection.