‘Father Christmas’ - The Kinks.
I like Carol of the Bells done by a boys’ choir and Sinatra’s version of Christmas Waltz. Barbara Streisand did a version of I Wondered as I Wandered that is fantastic. If you like jazz at all, Chet Baker has an instrumental of Silent Night that is really special. Top it off with Ray Charles and Winter Wonderland.
I concur that Judy Garland’s Have Yourself a Merry Little Christmas is the only way to go.
Fairytale Of New York, by The Pogues. Best Christmas song ever written, especially after a few drinks.
As far as Have Yourself a Merry little Christmas goes, the tops IMO is the recording done by John Denver and Rowlf the Dog.
“Christmas In Hollis” – Run-DMC
For a twist on the traditional, try Mel Torme’s version of Good King Wenceslas. Nice jazzy beat and…scatting!
Although I think that Judy Garland’s version of Have Yourself a Merry Little Christmas is the definitive one, I also like Ella Fitzgerald’s rendition.
And you can never go wrong with Christmas Blues by Dean Martin.
Baby, It’s Cold Outside–Nothing beats Liza & Alan Cummings on the “Home for the Holidays” CD.
Santa Baby–Jane Krakowski on the same CD.
Rudolph–How can that NOT be Burl Ives’s version?
The 12 Days of Christmas–John Denver and the Muppets (badump dump).
There’s a marvelous CD called “A Broadway Christmas” that has some great classicals and some less known Christmas songs (I Don’t Remember Christmas is my personal favorite).
Two words: Rosemary Clooney.
It doesn’t matter which songs (though I’m preferential to Let It Snow and White Christmas) just get yourself some Clooney. Seriously. It isn’t Christmas without Clooney.
The Vandals version of "Dance of the Sugar Plum Fairies is awesome.
So is the Vandals song “Christmas time for my Penis”
For a little something different, I love “Old Toy Trains” by Roger Miller (the *King of the Road * guy). Great song. Also Santa’s Gone (Milk 'n Cookies) by Clint Black, and ***Christmas ** * by Blues Traveler
But really, you *have * to have ***Please Celebrate Me Home ** * (Kenny Loggins or Al Jarreau).
Like the OP, I’m a traditionalist where Christmas music is concerned; I don’t like anything too snarky or hip-clever. That said, I still think the single best compilation CD you can buy is probaby Croon and Swoon: A Classic Christmas. Has a lot of the classics: Lena Horne’s “Let It Snow,” Johnny Mathis’ “Winter Wonderland,” Perry Como’s “No Place Like Home for the Holidays,” Judy Garland’s “Have Yourself a Merry Little Christmas” (don’t listen to that one if you have a lot of pills or a loaded gun in the house). I would supplement this album with:
“Merry Christmas,” Johnny Mathis (still his best XMas album)
“If Every Day Were Like Christmas,” Elvis
“A Charlie Brown Christmas,” Vince Guaraldi
“A Jolly Christmas from Frank Sinatra,” the Chairman himself
That covers most of your classics right there. I’ll leave the oddball stuff to others.
Ok. Great suggestions.
My album so far
Blue Christmas- Elvis Presley
Feliz Navidad- Jose Feliciano
Frosty the Snowman- Burl Ives
Hannukah Song- Adam Sandler (diversity and all)
Have Yourself a Merry Little Christmas- Judy Garland
It’s the Most Wonderful Time of the Year- Andy Williams
Jingle Bell Rock- Bobby Helms
Joy to the World- Frank Sinatra and Friends
Let It Snow, Let It Snow- Frank Sinatra
Mele Kalikimaka- Bing Crosby
O Come All Ye Faithful- Jim Nabors
O Holy Night- Jim Nabors
Rocking Around the Christmas Tree- Brenda Lee
Rudolph the Red Nose Reindeer- Gene Autry
Silent Knight- Bing Crosby
The Christmas Song- Nat King Cole
The Little Drummer Boy- Harry Simeone Chorale
Please Come Home For Christmas- The Eagles
Trying to Track Down
**Happy XMas (War is Over) **- John Lennon
Undecided
**Winter Wonderland[b/]- Will look at Mathis
Do You Hear What I Hear?- Looking a Nabors, but I getting “Gomer” heavy.
It’s Beginning to Look a Lot Like Christmas- Como?
Jingle Bells- I will look into the Count Basie Orchestra
Silver Bells- Bing? A neccessary song, but Bing croons a bit too much.
I’ll Be Home For Christmas- Lou Rawls?
I also think I need to listen to some more Nat King Cole samples. His versions go down easy.
You also might want to look at The Carpenters’ Christmas Collection.
***Merry Christmas, Darling ** * has always been one of my favorites.
I like the mambo version by someone, Billy May?
So many things to reply to. This is, of course, a sign that I think waaaaay too much about Christmas music.
DeVena, I didn’t know Roger Miller did a version of “Old Toy Trains.” It’s a really nice song, and I’m a fan of Roger Miller, so I’ll have to find it.
Southpaw, I love that Torme version of Wenceslas, though his Christmas version of “Glow Worm” is the one that always sticks in my head like taffy. I used to have a brass choir version of Wenceslas that I loved, too, but I can’t find it and don’t know who it was. sob
Zoe, I, too, like Streisand’s version of “I Wondered as I Wandered,” though I’m a bigger fan of Mahalia Jackson’s. Have you heard it?
coven, I’m convinced. I’ll check it out. My husband will not thank you for feeding my Christmas music addiction. 
kaylasdad99, you say Der Bingle, I say the Bingster. Instead of calling the whole thing off, we’ll swap Christmas music. I love Rockapella so I bet I’d love their “Silver Bells.”
Check out Frank’s version. I’ve never liked this song 'til I heard his recording. “I love those J-I-N-G-L-E Bells!”
Check out Ray Conniff’s version; it’s available on the album I mentioned in my first post.
Please check out *God Rest Ye Merry Gentlemen * by Barenaked Ladies and Sarah McLachlan! You won’t be sorry!
From A Christmas Gift for You from Phil Spector:
White Christmas - Darlene Love
Santa Claus is Coming to Town - The Crystals
Frosty the Snowman - The Ronettes
Christmas (Baby Please Come Home) - Darlene Love
I Saw Mommy Kissing Santa Claus - The Ronettes
This album has some of the best version of these songs.
2000 Miles - The Pretenders
Kidnap the Sandy Claus, What’s This?, and Making Christmas - Nightmare Before Christmas soundtrack
It’s Christmas Charlie Brown (the whole CD) - The Vince Guaraldi Trio