I decorate for Thanksgiving with natural materials from around the house. Granted I have 25 acres to scrounge from, and that's 1 thing I am truly thankful for.
I have a grapevine cornucopia that I freshen up every year and I string the dining room light with leaf garland. I keep pumpkins around the house and scarecrows here & there, as well as indian corn and bowls of preserved leaves and pine cones.
Mostly though it's food. I put out a big bowl of different nuts with nutcrackers to munch on the week before, and lots of cheeses and crackers on different days.