There are a variety of mens' hats in formal wear that I can think of: bowler hats, fedoras, Hombergs, and top hats.
There are also a variety of mens' hats I can think of that are associated with informal wear: cowboy hats, newsboy caps, flatcaps, and berets.
But, as far as I can tell, it is extremely uncommon for anyone to wear these in Europe or North America today. When people do wear them, it is usually to make some kind of fashion statement (merely by virtue of wearing the hat, not by virtue of anything about the hat itself). The formal hats especially seem to be particularly taboo for men to wear these days (i.e. I get the impression it would be difficult to be taken seriously while wearing a top hat)
What led to the decline of mens' hats and when did this occur? I imagine it was some time in the 20th century, but I'm not sure when or why exactly.
From the faqs.