I've noticed a nice upswing in alternative items being discussed here from Shorty's hat to Indy's turban, and being an old Boy Scouter, I wanted to throw in that Miller Hats is finally selling a great campaign hat that looks very close to style worn by River Phoenix in Last Crusade.
Most campaign hats have a pancake flat brim, but the young Scouts of the early 20th century up through the 40s rarely wore the flat brimmed "Smokey the Bear". Most preferred the floppier hats like River's as did my grandfather when he was a kid. This Miller campaign hat seems to fit the bill, with only a metal Scout insignia needed and a removal of the "ribbon".