I grew up with lots of traditions, most of which we still keep when I go home for Christmas.
Dad, wearing a nifty Santa-hat or reindeer horns, distributes the gifts one at a time. Then for dinner we pop our Christmas crackers, don our paper crowns and make fun of the lame prizes and jokes as we eat our dinner. The dinner has changed over the years, but yorkshire puddings are almost always on the menu. After dinner, the jigsaw puzzle!
Can't say I really have any New Year's Eve traditions. These days I'm usually asleep way before midnight...