My family celebrates Thanksgiving, but not always on Thanksgiving Day. That started back when I was a missileer (1987-1991); since I had small children then, I would usually volunteer to pull alert on both Thanksgiving Day and either New Year's Eve or New Year's Day if I could have both Christmas Eve and Christmas Day off. (The single missileers often volunteered to pull Christmas Eve/Day alerts of they could get New Year's Eve/Day off; it was more important to them that they be able to drink in the new year, and they tried to cover Christmas for those of us with families at hand.) So we'd have our Thanksgiving later, usually on the Saturday following the actual holiday.
Nowadays, it's because my wife is a bit older, and she likes to prepare a fancy Thanksgiving breakfast, which usually takes enough out of her that she's not up to doing the full Thanksgiving feast on the same day. So the holiday's always been pretty flexible for us, as far as what day the actual meal falls on.
Johnathan