At my workplace, the lobby music has “I Wanna See Santa Do the Mambo” in heavy rotation.
“Grandma Got Run Over By a Reindeer”, hands down. (I won’t even link to it.)
Santa Doesn’t Cop Out on Dope by Martin Mull.
“Grandma got run over by a reindeer,
Walking home from our house Christmas Eve,
You may say there’s no such thing as Santa,
But as for me and Grandpa, we believe.”
It does wear out its welcome quickly.
At Target I was looking at a CD collection of modern Xmas songs. The second to last track was The Bangles Hazy Shade of Winter. Just 'cause it has ‘winter’ in the title does not mean it is Christmas music, guys.
I thought I was going to win with 'Little Saint Nick" by the Beach Boys, but I guess not.
Brad Paisley “Kung Pao Buckaroo Holiday”
Leroy the Redneck Reindeer
The newest silly Christmas song has got to be Annie’s song on Community. It’s “interesting.” Here’s a YouTube link: http://www.youtube.com/watch?v=rwsATai–yg
Porky Pig’s outstanding rendition of Blue Christmas:
The cast of Avenue Q’s lovely rendition of The Holi-Daze-a song that got cut from the show, but is on the 2008 Carols for a Cure
When the crowds abound at the holidays
And you feel like throwing a fit.
You can merrily watch them light the tree
If you’re already lit.
When Santa shows up for the holidays
And you know he’s in on the gag.
He’s up on the roof full of 90 proof.
He’s always half in the bag.
All of the 13 CfaC CDs have some specially written songs on them, and it’s for a good cause.
A Spaceman Came Travelling - Chris DeBurgh. I wonder if he gave Von Daniken a credit?
Mind you, the plastic Paddy cover version by Celtic Woman has me laughing and trying to hold back vomit at the same time. 
“Look who’s coming round the bend
It’s Santa and his reindeer friends
With a ho-ho-ho and a hey-hey-hey
It’s Santa’s Super Sleigh!”
Jonathan Coulton’s “Chiron Beta Prime”
“Jingle Bells” by the Singing Dogs, hands down.
Also worth noting that it’s a Paul Simon composition (for S&G) with an intentionally ‘down’ theme.