If you think about it, Thanksgiving is a naturally frugal holiday. The focus is all on food and family, not expensive gifts or decorations.
The food served is cheap: turkey (39 cents to 59 cents a lb. right now), mashed potatoes (about $5 for a huge bag) and stuffing (great stuff considering it's made out of old, stale breadcrumbs). Typically, relatives each bring something, so you don't even have to spring for the whole feast. Want some wine with your meal? Two Buck Chuck makes a couple of great varietals that go well with turkey. A local grocery was advertising pumpkin pies for $2.99. I can't even make them for that price!
Decorations can come from nature. Pick up some beautiful fall leaves, acorns and pine cones, and use them to dress up the house.
Build some family traditions by having family members all sign an inexpensive tablecloth with permanent marker, then use it year after year, and add to it, making note of any special family events or milestones each year. Start a Thankful Jar. Have each family member write something they are thankful for this year on a slip of paper, stick them in a jar, and then read them aloud.
After dinner, turn the football game on, or dig out those dusty board games. Nothing gets people talking like a game of Pictionary or Trivial Pursuit. Converse with your extended family members and really catch up.
Relax, enjoy yourself, and take some time to be thankful for this most frugal of holidays!