If I knew what I was doing, I'd be posting those nifty YouTube viewing windows to share a few of my favorites with you, but I can't see to work out the particulars. So... I shall give you links instead.
1. Christmas Eve / Sarajevo -- Trans Siberian Orchestra
This is an instrumental masterpiece, plain and simple. Orchestrated like a grand piece of fine art, it incorporates modern instruments, synthesizers, upbeat tempos, and too many other good things to list. It's popular with people who like to synch their Christmas lights to a musical track, but this link goes to a recording from one of their concerts. It's got the cleanest audio of the clips I've seen on YouTube.
2. The Little Drummer Boy -- the Animaniacs
Arguably the best cartoon ever animated (American, at least. I maintain that Danger Mouse is the best internationally), the Animaniacs was a show from the 90's produced by Steven Spielberg. It was the adventures of three siblings (the Warner bros. and their sister) who lived in the water tower on the studio lot and generally wreaked havoc with everything and everyone. I think Pinky and the Brain are probably the best known segment, but one year, they did a Christmas special, including the clip I've linked here. It's their own take on the Christmas carol with Wacko (*cough* Ringo *cough*) playing the part of Drummer Boy. Soon the whole manger's rocking to a swing-style rendition of the tune. Truly unique, and memorable.
These last few are the songs I listen for every year on the radio when our local country station plays their Christmas marathon. ( I was raised on classic country music, so my "traditional" listens mostly come from that.)
3. Pretty Paper -- Willie Nelson
I can't explain why I love this song, because it's exactly the sort of sentimental song I usual detest, but I have to hear this song at least once a year, or else it's just not Christmas.
4. Happy Christmas / War is Over -- John Lennon
Celine Dion has a decent remake of this song, but I'm going with the original. It's not a happy song, and is rightfully melancholy for the content, and it's absolutely one of my favorite Christmas songs ever.
5. Blue Christmas -- Elvis Presley
I admit it. I listen to this one to laugh. I love hearing it on the radio, but it makes me giggle. (Yes, I know it's shocking, but I CAN giggle :-P )
6. Christmas in Dixie -- Alabama
Another semi-sentimental one, but still worth a listen.
7. Hard Candy Christmas -- Dolly Parton
Yes, it came from a movie about prostitutes, but I don't care. The song is something I like to hear. Deal with it.
8. All I Want for Christmas is You -- Vince Vance & the Valiants.
My all time favorite Christmas song, bar none.
9. Christmas Time in Texas -- George Strait
Do not badmouth George Strait. Just don't. There are laws. (Not the best audio.)
10. Baby it's Cold Outside -- Glee
A new favorite, sung by Chris Colfer and Darren Criss. Yes, they're both guys, but I defy a female to sing this song as well as Chris C.
I found videos with the songs doing a quick search, I didn't watch them all the way through.