We typically sing the first half of each stanza, and the refrain is the last half of the first stanza.  We miss the richness of the halves of the stanzas that we do not sing, especially the second half of the second stanza, which answers the questions what Child is this, and why did He come?

http://www.youtube.com/watch?v=Oz44GJlSPeo&feature=player_embedded