The Muppet Christmas Carol
A Christmas Carol (1984)
A Christmas Carol (1938)
They're all versions of the same story, but it's the best Christmas story and even one of the best stories, period, IMO. I also love the 1951 version and many of the other list choices (and a few movies that didn't even make the list, like The Shop Around the Corner and Holiday Inn), but we were asked to choose only three Christmas movies and those are the three that I watch most often.
BTW, if anyone's interested, the 1951 and 1984 versions are both on YouTube: