Historically we've always watched Going My Way and The Bells of St. Mary's during the holiday season. Since being little on my grandfather's lap I've always had a soft spot for Der Bingle and I could watch Ingrid Bergman in a dish soap commercial.
The other two must watches are The Snowman and A Child's Christmas in Wales. The Snowman is a beautiful little thing, wonderfully scored by Howard Blake and produced by John Coates which always makes me chuckle. A Child's Christmas in Wales is of course a poem by the great Dylan Thomas and the film adaptation features Denholm Elliott.