Examples include, of course, this one by Straight No Chaser, which gets tons of airplay every year:
And then there's the Canadian Brass, with a version that should appeal to classical music lovers (especially brass players):
I heard this rendition -- actually pretty much a new song, based on the original, with a dark twist -- just last night on the radio:
Of course, you have John Denver and the Muppets, who don't do much to "comedify" the song other than play up the personalities of every single muppet who participates. I appreciate this minimalistic approach to being funny!
It wasn't always like this, though. For nice, straight renditions of Christmas songs, the go-to is almost always Mr. Crosby:
And finally, the mighty forces of the Mormon Tabernacle Choir and friends.