Although not strictly a Christmas carol, Jesus Christ the Apple Tree gets more air time at this time of year than any other, probably because it has some wonderful choral settings that choirs like St. Olaf's really do well. Elizabeth Poston's arrangement ranks as one of my favorite pieces ever.
The text is from 18th century New England, and -- like other carols that portray Christ as a rose -- emphasizes the sheer beauty of the savior. The text calls to mind the famous second verse of Beautiful Savior: fair are the meadows, fair are the woodlands, robed in flowers of blooming spring; Jesus is fairer, Jesus is purer. He makes our sorrowing spirits sing.
Though this kind of piety sounds old-fashioned to some, beauty is a theme with renewed popularity among theologians now. Given that it is increasingly difficult to make empirical truth claims of any kind these days, we could do worse than to emphasize the sheer beauty of having a savior who takes on our humanity.
A slightly less serious observation: according to Michael Pollan in Botany of Desire, apples in early Americana were not grown for schoolchildren's lunches. Johnny Appleseed was celebrated for taking apples across the country becauase apples were a source of cider -- that is, hooch. So in this sense, Jesus as an apple tree is analogous to Jesus as a vine. His final gift to us isn't just sustenance in the puritan sense -- it is drink, it is joy.