Note: The Amazon links no longer take you to pages for the songs. I don't know why Amazon had to change its whole music setup, but it's annoying. Still, I'll leave the links here instead of deleting them just in case they decide to change back someday.
All I Want For Christmas is You - Mariah Carey (Amazon)
All My Bells Are Ringing - Lenka (Amazon)
All the Gifts I Need - JD McPherson (Amazon)
The Angel Gabriel - Amanda Palmer (Amazon)
Angels We Have Heard on High - Point of Grace (Amazon)
Auld Lang Syne - Barenaked Ladies (Amazon)
Away in a Manger - Mindy Smith (Amazon)
The Bell Medley - Classic Christmas Singers (iTunes)
Blue Christmas - Elvis Presley (Amazon)
Bring Me Love - John Legend (Amazon)
Carol of the Bells/Sing We Now of Christmas - BarlowGirl (Amazon)
Carol of the Bells - Emmy Rossum (Amazon)
Carol of the Bells - Pentatonix (Amazon)
The Cherry Tree Carol - SimpleGifts (Amazon)
The Chipmunk Song (Christmas Don't Be Late) - David Seville and the Chipmunks (Amazon)
Christmas (Baby Please Come Home) - Darlene Love (Amazon)
Christmas Must Be Tonight - The Band (Amazon)
The Christmas Song - Nat King Cole (Amazon)
Christmas the Whole year Round - Sabrina Carpenter (Amazon)
Days Gone By - Applejack, Apple Bloom, & Granny Smith (Amazon)
Ding Dong Merrily on High - Jackie Evancho (Amazon)
Do You Hear What I Hear? - Home Free (Amazon)
Don't Start Without Me - The Fizz (Amazon)
Father Christmas - The Kinks (Amazon)
Feliz Navidad - José Feliciano (Amazon)
The First Noel - Lady Antebellum (Amazon)
Frosty the Snowman - Cocteau Twins (Amazon)
God Rest Ye Merry Gentlemen/We Three Kings - Barenaked Ladies & Sarah McLachlan (Amazon)
Good King Wenceslas - The Irish Rovers (Amazon)
Grown-Up Christmas List - David Foster feat. Natalie Cole (Amazon)
Gruss Vom Krampus/Krampus Karol of the Bells - Brea Olinda High School Singers (from Krampus) (Amazon)
Happy Xmas (War Is Over) - John Lennon (Amazon)
Have Yourself a Merry Little Christmas - Kelly Sweet (Amazon)
Here Comes Santa Claus - Elvis Presley (Amazon)
Here We Come a Caroling - Classic Christmas Singers (iTunes)
Hey Santa! - Carnie and Wendy Wilson (Amazon)
Ho Ho Ho - Liz Phair (Amazon)
I Wish It Could Be Christmas Everyday - Wizzard (Amazon)
I'll Be Home For Christmas - BarlowGirl (Amazon)
It's Beginning to Look a Lot Like Christmas - Bing Crosby (Amazon)
It's Christmas Eve - Alex Khaskin (Amazon)
It's the Most Wonderful Time of the Year - Martina Sorbara (Amazon)
Jingle Bells - William Shatner feat. Henry Rollins (Amazon)
Joy to the World - Pentatonix (Amazon)
Last Christmas - Carly Rae Jepsen (Amazon)
Let It Snow - Luscious Jackson (Amazon)
Little Drummer Boy - Pentatonix (Amazon)
A Mad Russian's Christmas - Trans-Siberian Orchestra (Amazon)
The Man with the Bag - Kay Starr (Amazon)
A Marshmallow World - Dean Martin (Amazon)
Mele Kalikimaka - Jimmy Buffett (Amazon)
Merry Christmas Baby - Otis Redding (Amazon)
Merry Xmas Everybody - Slade (Amazon)
The Most Wonderful Day of the Year - Glee Cast (Amazon)
Nutcracker - Straight No Chaser (Amazon)
O Come, All Ye Faithful - Jillian Edwards (Amazon)
O Come O Come Emmanuel - Enya (Amazon)
O Holy Night - Leigh Nash (Amazon)
O Little Town of Bethlehem - Jewel (Amazon)
O Tannenbaum - Celtic Woman (Amazon)
Omedetou Christmas - Peach Hips (by the cast of Sailor Moon)
Please Come Home For Christmas - Charles Brown (Amazon)
Punk Rawk Christmas - MxPx (Amazon)
Santa Claus Is Coming to Town - The Jackson 5 (Amazon)
Santa Loves to Boogie - Asleep at the Wheel (Amazon)
Santa Tell Me - Ariana Grande (Amazon)
Season's Freaklings - Bunnygrunt
Silent Night - Kelly Sweet (Amazon)
Silver Bells - Doris Day (Amazon)
Sleigh Ride - Karmin (Amazon)
Sleigh Ride - The Ronettes (Amazon)
Someday at Christmas - Stevie Wonder (Amazon)
Toy Packaging - Sara Groves (Amazon)
Very Merry Christmas - Dave Barnes (Amazon)
We Wish You a Merry Christmas - Shonen Knife (Amazon)
Welcome Christmas - The Clumsy Lovers (Amazon)
Welcome Christmas - Glee Cast (Amazon)
What Christmas Means to Me - Stevie Wonder (Amazon)
White Christmas - Kelly Sweet (Amazon)
Winter Wonderland - Kate Havnevik (Amazon)
Winter Wonderland - Sleeper Agent (Amazon)
Wonderful Christmastime - Paul McCartney (Amazon)
You Make It Feel Like Christmas - Gwen Stefani feat. Blake Shelton (Amazon)
You're a Mean One, Mr. Grinch - Lindsey Stirling feat. Sabrina Carpenter (Amazon)