I don't know how many doughnut shops are taking part, but Krispy Kreme is. If you go to any of their participating establishments, you can get a free doughnut. Check their website here to find out the locations.
Here's a list of apparently all the participating organizations. Some require a purchase -- at Dunkin' Donuts, for instance, you have to buy a beverage. No purchase necessary at Krispy Kreme. I don't see Winchell's on the list, or anything about it on the Winchell's website, though I suppose that doesn't mean for absolute certain they aren't joining in the festivities.
By the way, not all the participating locations are doughnut chains. Even if Winchell's doesn't appear to be joining in, Jiffy Lube is! They're even giving free tire air pressure checks, along with a free doughnut at participating locations. (Apparently the tie-in is that the little spare tire you have in your car is also called a "donut" tire.)