I might lose some of you on my final two picks because they aren't popular recordings or standard carols. But they are Christmas songs nonetheless and I happen to enjoy them both very much. (I have also had the pleasure of performing them as well, which endears them to me even more so.)
Song Number Two on the list is a choral piece by Ralph Vaughn Williams called "Wassail". It's a four-part choral arrangement (that would be "written for soprano, alto, tenor, and bass" for those of you not in-the-know out there) that takes off in a very light-spirited romp from the beginning for the duration of the song. It's a fun listen and it's fun to sing.
You can hear it here (RealAudio required).