The Salvation Army started the celebration in 1938 to honor groups of people who served doughnuts to soldiers in World War I. There were volunteers, called Doughnut Dollies, who worked out of Salvation Army huts and provided, among other things, baked goods to our armed forces. Wikipedia has a whole entry on the history. Who knew?
It would be highly appropriate, then, to give a serviceman or a vet a doughnut (or two) today — especially since it's the anniversary of World Ward II's D-Day as well.