Typically, Thanksgiving Dinner at LykeBeer World Headquarters includes roast turkey, dressing, mashed potatoes, gravy, at least two vegetable dishes, and my mother's pies - pumpkin and apple at minimum; often pecan as well. If your meal typically includes other common Thanksgiving staples like sweet potatoes or green bean casserole, these recommendations will work as well.
Vienna Lagers, Marzen-style Oktoberfests, English Mild Ales, English Brown Ales, and American Brown Ales all have lovely roasted malt, melanoidin flavors that complement the roasted flavors in turkey and roasted vegetables because during the malting process, grain goes through the same Maillard-reaction browning process as your roasted foods do.
Dressing (or stuffing) and roasted vegetable dishes often include herbal flavors such as sage and rosemary. If your dressing includes mushrooms you will also get a pleasant earthiness. Saison and Biere de Garde are styles that work well with the herbal and earthy foods. These beers often display peppery or funky characteristics derived from the yeast strains used in making them.
Other styles that we've had good results with at the Thanksgiving table are Berliner Weisse, Flanders Red Ale, Oud Bruin, and Fruited Lambics such as Kriek (cherry) and Pomme (tart apple). Each of these beers has a tart or sour character that can cut through the richness and fattiness of many typical Thanksgiving foods. Alcohol and carbonation in any of the styles mentioned in this post also play a key role in scrubbing rich and fatty food residue from your tongue to ward off palate fatigue. While complementary flavors are particularly pleasant, I would caution you against matching flavors such as serving the Pomme Lambic with apple pie; you are more likely to cancel out the apple flavor rather than create an apple-driven flavor explosion.
Now if you are saying, "I wanted to know which beer to serve at Thanksgiving and you named a dozen beer styles." I would recommend starting out with one or two of the styles mentioned. Maybe start with a Vienna Lager or a Saison. Even better, serve them side-by-side; I often do. If you're feeling particularly ambitious, serve the meal with a flight of 4 or so of the styles. It turns out Thanksgiving happens every year so there is no need to try them all this time around. Give things at try, if you like it, go with it and have fun.