The first of the new Christmas Specials - 2005's The Christmas Invasion - gave us a specially written song - which would go on to provide the Tenth Doctor's first theme. Song for Ten was composed by Murray Gold and had vocals by The Divine Comedy's Neil Hannon. You'll find other versions around - with second-rate pub singer vocals. The Hannon version is by far the superior one. Then again, I'm a big Divine Comedy fan.
The following year Gold and Hannon collaborated again for The Runaway Bride - with Love Don't Roam.
It's marginally not quite as good a song - and certainly not as Christmas-y.