Growing up in my house, everything was always wrapped, including stocking items. The only thing that wouldn't necessarily get wrapped would be a stuffed animal. However, at my house, stockings are done on December 6th, when St. Nicholas comes (German tradition). However, when I was about 11, I found out that other kids got their stockings on Christmas, so I somehow managed to convince my parents that we needed to do stockings both days!
At DH's house, stockings don't get wrapped, and there is one Santa gift, and that isn't wrapped either. Even though the kids are now 28 & 33, Santa likes to bring a small toy or plushie.
We are usually at one of our parents for Christmas, so we don't really have traditions at our place. Except, that when St. Nicholas comes, we don't really do a stocking, just one small gift. That is either wrapped or unwrapped depending on where the wrapping paper is. This year, I didn't feel like digging out the tote, so it was unwrapped. St. Nicholas brought me the set of Doodlebug Flock. DH got new ear buds for his iPod, and a little Pirate
LEGO set. Our other thing, is that since my birthday is the 21st, birthday wrapping CAN NOT be Christmas paper. And we try hard not to have our little Christmas on my birthday. Although, one year we were flying out early in the morning of the 22nd, so we opened my birthday presents, went out to dinner, and then came home and did Christmas.