"Away in a Manger" is certainly a familiar tune to us, but some may not realize that this traditional melody was borrowed from an existing Johann Strauss waltz written about 19 years before the poem. Note the resemblance below starting at 2:48:
I'd also like to mention "Hark! The Herald Angels Sing." The words were written in 1739 by Charles Wesley – well, not exactly the ones we use today. Wesley's words were changed slightly by George Whitefield and later a portion of "Festgesang" by Felix Mendelssohn (a song written to commemorate the invention of movable type) was used instead of Wesley's preferred tune at the time. If you'd like to hear how the Christmas song might have sounded if Wesley had his way, you can play the video and sing along with the printed words below (the intro ends at about 0:21).
Hark, the herald angels sing
Yep, Wesley wanted his words to use the tune to "Christ the Lord Has Risen Today." Talk about confusing! It would be hard for me to keep Christmas and Easter separate. Although I do like Mendelssohn. If this has your mind all mixed up, here's a version with the traditional lyrics and Mendelssohn's music that you probably recognize:
"Glory to the newborn King!
Peace on earth and mercy mild
God and sinners reconciled"
Joyful, all ye nations rise
Join the triumph of the skies
With the angelic host proclaim:
"Christ is born in Bethlehem"
Hark! The herald angels sing
"Glory to the newborn King!"
There's also a Mendelssohn connection to another Christmas tune. "It Came Upon a Midnight Clear" is usually set to the "Carol" by Richard Storrs Willis who was trained by Mendelssohn.
So, while I agree with most of you that I like the familiarity of traditional Christmas songs, I also like to hear creative adaptations of these tunes, because they get me to focus on the lyrics which are also beautiful in their own right.