Not the Wednesday before. Or, the weekend prior, for that matter (Nov 22-23, this year, btw). But you already knew this.
No, assuming your schedule allows it, the Monday or Tuesday before Thanksgiving is your best bet for scoring the cheapest fare to grandma's house. At least according to data recently crunched by Priceline.com. Which, shouldn't come as much of a surprise.
As for return flights? Well, travelers who argue with their parents and are happy to skip out mid-meal before the Cowboys even kick off are in the best spot -- flying home on Thanksgiving Day or Black Friday is your cheapest move (even if it means missing $12 laptops at Walmart at 3am). Or, if you love your parents and can't get enough of family bowling nights, stick around until Tuesday, December 2. Prices drop after the Sunday/Monday rush.