I have for long played my alltime favorite Wing Commander 1 couple days before christmas, except when I've recently played some other game of the series. But I'm just about to give up that tradition, along certain others related to the series.
I do always play a bit Christmas Lemmings demos 1991-1994.
Because I got my Master System for christmas, but actually few weeks early, I always have it out annually this time of year for a month or so. But not really specific christmas tradition there.
There's a small old Finnish adventure game - something someone just made up quickly - roughly translating "Santa's Christmas Hangover" that I do often look up:
Additionally there's Slick'n'Slide, a little shareware driving game with tons of tracks. As each track has top 10 records, at the end of year I like to try to get couple more records in before year changes. That's not typically right at christmas, but often some too.
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