We have wild game for Thanskgiving quite often, but this year we cooked a domestic turkey, since due to unfortunate circumstances we didn't get to go turkey hunting this spring, and didn't have a wild one left in the freezer.
A few years ago we started a new "tradition" at our house. Thanksgiving week is the last of Montana's 5-week rifle season for deer and elk, and by then we've been hunting since at least early September. We're getting a little weary, and while we may go out Monday and Tuesday, we don't like to fight the crush of last-minute hunters that normally occurs from Wednesday through the weekend. Instead we're ready to take it relatively easy, or at least as easy as two obsessive-compulsive people can.
So we cook Thanksgiving dinner on Monday afternoon, keeping it simple, and live off leftovers, including various recipes Eileen develops for turkey later in the week. This weekend we also "celebrated" by cutting up the mule deer buck I killed on the 16th, which had aged sufficiently--and almost topped off this year's freezer. (We have two 15 cubic-foot chest freezers, one next to the kitchen, filled with meat from previous years, and another in the basement, which we try to fill up during the present year. The mule deer almost topped it off.)
Of course, all hunting doesn't end with Thanksgiving week. I'm leaving for South Texas pretty soon, and am assigned the task of "harvesting" enough wild pork to completely fill the basement freezer. We'll also be hunting birds through December.