My family's tradition is to watch all of the Doctor Who Christmas specials... which were recently removed from Prime.
Santa Claus is Comin' to Town - the 1970 classic stop animation. Burgermeister Meisterburger has outlawed toys in Sombertown.
Fireplace for your Home Christmas Music edition or The Merry Yule Log
NOT: The Miracle On 34th Street. The Prime version is a 1950s TV remake of the 1947 classic film.
Sorry, Prime has canceled Christmas.
I would take advantage of these now since I've been monitoring them every day and Amazon seems to randomly take some offline and mark them as unavailable. Let me know if I missed any or screwed up a link. I just wanted to put all these in one place.
Currently available titles:
Abraxas, Guardian of the Universe
Plan 9 From Outer Space: Live!
Manos: The Hands of Fate Live!
Rudolph The Red-Nosed Reindeer
Night of the Living Dead: Live!
Additionally, there is a channel on Amazon Prime Video, called CONTV. You can do a 7-day trial for free, then after that it will charge the card associated with your Prime account $4.99 a month. Cancelling takes a single click. I HIGHLY recommend checking out the channel just so you can take advantage of Birdemic: Live! - it was hilarious, for me they were at their absolute best and I love hearing the audience laughing along with the jokes.