My favourite, too!
Followed by Snoopy’s Christmas.
Another vote for “Fairytale of New York”.
“Father Christmas”-The Kinks
Dan Hicks & The Christmas Jug Band “Somebody Stole My Santa Claus Suit”
On Christmas Day you can’t get sore.
Your fellow man you must adore.
There’s time to rob him all the more
the other three hundred and sixty four.
put me down as another Tom Lehrer fan.
Christmas Cookies, by George Strait.
Christmas in Sarajevo by Trans Siberian Orchestra.
O Holy Night by Mr. Michael Crawford.
Mary’s Boy Child by Bony M.
I get goosebumps from hearing each of these. Every single year. Always.
For more mundane Christmas songs, I really like hearing Walking In A Winter Wonderland - by anybody! (Just the idea of spending a Christmas with my honey in a snowy cabin, with a fireplace, nothing to do but take a walk in the snow when we need to get some air - must be heaven!)
And God Rest Ye Merry Gentlemen. The Annie Lenox video is beyond awesome!
I really like Stille, Stille, Stille, by the Vienna Boys’ Choir. Can’t find it on YouTube.
For fun enjoyment I like Baby it’s Cold Outside. Everytime I hear it, I picture a 60’s style couple teasing back and forth if she should leave or stay and face the scandal! Dean Martin/Doris Day type of characters.
For sentimental enjoyment I like Silent Night. My dad had voice that could bring tears to your eyes when he sang this song (in a good way 
) It’s a very emotional song for me.
I’m not sure if you’re kidding, but I actually like that one! It really captures that Xmas excitement.
More serious - O Holy Night - Pavarotti
Less serious - 12 Days of Christmas - The Yobs (On the first day of Christmas my true love gave to me, a vibrator with a battery).
Some people (okay, Cracked.com) consider that the date rape Christmas song 
Haha; I have a little more innocent mind, I guess. I think that she wants to stay; but knows that to be a good girl she shouldn’t. He of course wants her to stay and is gently chiding her into it.
What’s funny is when I clicked on your link; I honestly didn’t know who sang the song. When I said Dean Martin and Doris Day; they were just who I thought of based on my watching their movies when I was a kid.
When George gets to this part, “Some disappear to who knows where, but I make sure that I get my share, and them kids just stand there waiting for the ones I miss.”, I just want to smack him and say, “Those cookies are for the kids!” 
God bless you and him always!!! 
Holly
I’m also very fond of Carol of the Bells.
My favourite seems to change every year. One year it was Peter Warlock’s “Bethlehem Down,” another year it was “Gesu bambino.”
I think I’ll have to go with “Fairytale of New York.”
“Santa Claus and His Old Lady” by Cheech and Chong
My new favourite,
The season is upon us by the Dropkick Murphy’s
I also love “White Wine in the Sun”! Minchin has an interesting perspective on things.
“O Come, O Come, Emmanuel”, “The Angel Gabriel” and “Keep Christmas With You” (from the Sesame Street Christmas special) are right up there too.
Generally speaking, my likes in this regard lean heavily towards hymns and not so much towards contemporary secular music.
Walkin’ 'Round in Women’s Underwear. (NSFW and loud)
I Believe in Father Christmas by Greg Lake.
I’ll go with Darlene Love singing Baby Please Come Home
She’ll be doing this Friday night on David Letterman.