Bing's "Do You Hear What I Hear?" always reminds me of "Gremlins"
since it was used in the kitchen attack scene. Great use of the song and gives it some bonus points (though it's always been one of my favorites as well). Though in general, I don't really have favorite Xmas songs, mainly just ones that annoy me and others that I mostly just tolerate because they're catchy and/or I have a nostalgic attachment. But Nat's definitive version of "Chestnuts" is definitely up there for me as well. Also gotta mention "Christmas In Hollis".
But as far as favorite Xmas *albums*, in addition to the Duke Ellington "Nutcracker Suite" and "The Beach Boys' Xmas Album", I've of course always been partial to "Charlie Brown Xmas" and like Tabs, I have a soft spot for carols performed by The Choir At King's College, Cambridge. Ella Fitzgerald's xmas album seems cool but I've only heard a few cuts. The Ginuine Xmas album is also good for a laugh, as is Dylan's.