Have you guys ever done a family version of Secret Santa? If you haven't then that might be fun. For anyone that doesn't know what that is, it's where everyone involved picks another person's name randomly ahead of time (usually out of a hat, but if it's family and they're spread out, it could be picked for them by the organizer and then e-mailed) and they're in charge of getting that person their Christmas gift. Usually this is done in offices and in military commands (where I picked it up), but it could be done by family too. It's even more fun if you don't reveal who each person's "Santa" is and have a guessing game taking turns to try to find out.
That's the only one I can think of. We play a lot of games at Christmas, just not centered around gift giving. I hope you get a lot of good ideas, I'll be coming back to see what other mommies have posted.