United States
United States Marine Corps drill instructor's campaign hat
This is an older hat (or "cover" as they call it in the Marines), probably from the 40’s. I don’t think anybody except drill instructors (USMC equivalent of Army sergants) wear them these days, but back around the time of WWI, this was standard-issue headgear. However many civilian and police organizations use this design today and they’re often referred to as “Smokey the Bear” hats. Officer-versions generally don’t have the rows of stitching around the crown and have bullion cords around the hat band which end in two acorns.

By the way, The drill instructor cover (hat)is called a "Smokey the Bear" due to the fact that United States Park Rangers wear the same cover. When a young bear cub, later named Smokey, was rescued from a forest fire, the bear was photographed with the cover on his head. Since then, the bear has become a symbol of fire safety and the hat has become known as the "Smokey Bear". Many thanks to my pal Paul of the USMC for filling in the details!