Personally, I like Tim Minchin's "White Wine in the Sun" and Nick Lowe's "Christmas at the Airport", but neither of them is particularly well-known.
At a higher cultural level, Handel's "Messiah" is always popular.
In America, other common christmas songs include "Rudolph the red-nosed reindeer", "chestnuts roasting on an open fire", "silent night, holy night", "good king wenceslas", "over the fields and through the woods", "mary did you know", "jingle bells", "Feliz Navidad", "O come all ye faithful", "all I want for Christmas are my two front teeth", and many, many others.