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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.
Famous bowler hat, symbol of working but also upper classes as well, a better cowboy hat than a cowboy hat started as a hard hat for gamekeepers. You can read more about history of bowler hats here.
Hats are a part of human wardrobe for centuries. With different uses, from protection to fashion statement they changed through time and changed with how we see ourselves. Learn more about history of hats.