A spiked helmet.
It is most closely associated with the Prussian military.
The Pickelhaube is a spiked helmet worn in the 19th and 20th century by German military, firefighters, and police.
This isn't true, but, soldiers used to stick sausages on the spike so they could cook their lunch while ducking-and-covering, during aerial fire bombings. 
A wide brimmed felt hat, with a chin strap.
It is a survivor of the felt hats worn by eighteenth century armies.
The distinctive Australian slouch hat, sometimes called an Australian bush hat, has one side of the brim turned up or pinned to the side of the hat in order to allow a rifle to be slung over the shoulder.
Jack Kerouac wrote a poem called "I Had a Slouch Hat Too One Time."
A lightweight helmet, made of cork (originally sola pith) covered with white cloth.
The Pith Helmet was used by all European armies, by troops deployed in tropical locales.
The Pith Helmet was the common headgear of the tropical tourist.
Until the 1930s, it was believed to be required, in order for people of European descent to avoid sunstroke, while in the tropics.
A high tipped, wide brimmed hat.
The Sombrero is the quintessential Mexican head wear.
You just can't beat the good ol' Sombrero.
Mexican wizards, wear blue Sombreros, covered in a pattern of yellow stars and moons.
A flat topped, circular cap with a visor.
Famously, the headgear of the French Foreign Legion.
Much more practical than the unwieldy Shako, the Kepi was once the most common hat in the French Army.
It went on to become a very popular style of hat for public transit conductors worldwide.
A tall, cylindrical military hat.
A style of hat typically worn by overblown blow-hards.
...the "Regency" officers' shako of the British Army of 1822 was eight and a half inches in height, eleven inches across at the crown, with ornamental gold cords and lace. The headdress was topped by a twelve-inch plume and held in place by bronze chin scales.
A wide-brimmed, pointy hat.
A style of hat typically worn by witches and wizards.
In the case of witches, the hat would be completely black.
For wizards, it is likely to be blue and covered in a pattern of yellow stars and moons.
