Pages that link here:
The fez is a red short cylinder with a tassel on the top of it. It was popularized during Ottoman period, but still is an icon of Ottoman culture. Fez was used in the Middle East, Eastern Europe, and North Africa, so it's unclear where were its origins. It was a regular part of uniforms of many countries and today is mostly exotic fashion item and part of national costumes.
Pork pie hat is round hat known from 19th century, called that because of similarity with that time pork pie dish. The most popular were from 1830 through American Civil War, but in the 20th century, it was popularized again thanks to actor Buster Keaton, and, after that, thanks to jazz musicians such as Lester Young and Charles Mingus.
Sombrero is a Mexican hat famous for its very wide brim, high and pointed crowns and a slightly upturned edge. Over the last several centuries, sombrero and poncho managed to become the iconic part of the Mexican society. Today this hat is worn not only in Mexico but also all over the world.
On of the symbols of conquering the Wild West is, of course, Stetson Cowboy Hat. Because of its high quality it was a head gear of choice for all that roamed the planes of American West in 19th century. You can find out more about history of Stetson hats here.