I may be an atheist, but I still like a lot of Christmas music -- for the tunes and the associated holiday memories, of course!
Something I really like in a melody is when it has an interesting shape to it. Imagine creating a graph, with time on the horizontal axis and pitch on the vertical axis. Songs with melodies that stay close to being a horizontal line can be pretty boring. (I say "can be," because it all depends on what is happening in addition to the melody.)
Some of my favorite holiday songs that have good shapes to them include Silent Night, Joy to the World, and God Rest Ye Merry Gentlemen.
I've always had a soft spot for Silent Night. It's a very soothing lullaby (which goes well with the sentiments of the lyrics). Here's a graph of the song, almost as described above -- note number on the horizontal axis, and pitch on the vertical axis:
I unfortunately could not figure out how to get it to display this graph with the actual measure numbers on the x-axis -- this is what I get for not using an actual graphing program!
But you can see the general arc of the melody, even if the scaling of the x-axis is not quite right. At the end, we have a climatic rise followed by a climatic drop. The melody hints at this from the beginning -- "Silent night/holy night" is a miniature preview of the last two phrases ("Sleep in heavenly peace/Sleep in heavenly peace"). Likewise the middle previews this: we begin to soar with "Round yon virgin" but come back down to the baseline with "mother and child."
You can see these parallels on the graph: from about 33 on the x-axis to the end is the big finale of the melody. You can see a similar shape at the very beginning (1 to 4, repeated immediately), and in the middle (15 to about 24, also repeated).
Joy to the World takes a different shape -- it's kind of like a V or W shape. The first line ("Joy to the world, the Lord is come") descends an entire octave, the second one ("Let Earth receive her King") comes right back up. Then we have a few descents ("Let every heart" and "Prepare him room"), followed by some ascents, modulating downward (the first two "And heaven and nature sing" lines), followed by the octave-jumping and ultimately descending final phrases ("And heaven and heaven and nature sing").
The grandiosity of Joy to the World is very similar to the final movement of Beethoven's 5th Symphony, which follows the same octave-spanning, V-shaped melodic concept (although the symphony is more like an upside-down V, because its melody ascends first and descends second). But this octave-spanning movement up and down the scale is part of what makes many melodies very grandiose and pompous (which I don't mean in a bad way). Other examples include "The Star-Spangled Banner," "Pomp and Circumstance," and Mendelsohn's wedding march from A Midsummer Night's Dream (a staple of American weddings alongside Pachelbel's Canon).
My favorite movement of my favorite Sibelius symphony -- the third movement of the Fourth symphony -- also uses the (inverted) V-shaped melody spanning an octave, but turns the grandiosity on its head by making it a minor octave rather than a major octave. (I hope to share this symphony with you at some point -- but it is an acquired taste. The first time I heard it I was like, WTF?!?! But I gave it a few more listens and fell completely, head-over-heels in love. It is the leader on play count in my iTunes collection, and by a long shot. This is saying a lot because this symphony is more than a half hour long.)
But I digress.
God Rest Ye Merry Gentlemen has an interesting arching shape to its melody, more like Silent Night than Joy to the World. But what sets this song apart to me is its minor key. I've mentioned before, I'm a sucker for something a little surprising or different, and this song does that by being in a minor rather than major key. It is also great fun to harmonize against, because there are so many ways you can go. I have fond memories of playing God Rest Ye Merry Gentlemen with my sisters when we were kids -- me on the violin, Rachel on the cello, and our younger sister on the viola or singing. Usually she would be the one to play the melody, while Rachel and I harmonized. Rachel had a good bass line that she would do, and I would tend to try something different every time. Ah, yes. Good times with music!