Christmas Eve happens to be my brother-in-law's birthday (bummer?), so the family gathers at my sister's house for a big birthday party, and at midnight we open a few presents for Christmas, then we resume partying.
Any unopened presents get unwrapped at home on Christmas day upon our return or when we wake up.
A personal tradition for me: I do a massive room clean-up (out with the old, in with the new) on New Years' Eve, so that I welcome the New Year with a spotless, super-clean environment in my room.
However, this year there may be a party that day with some friends for which they'd really want me to go, so I might clean my room on the 30th instead.