Beefeater’s…Beefeater’s…B…never mind.
Diver’s red wooly cap - as sported by Jacques Clouseau, the famous bungling underwater detective
Accountant’s green eyeshade
The garrison cap AKA “cunt cap” is associated with the military.
Those caps that doctors and nurses wear during surgeries.
Batting helmet.
Traditional Congolese leopard-skin cap made famous by Mobutu Sese Seko during his ceremonial appearances as head of state.
Roman Centurion’s galea.
Since it’s been a few hours since my last one, may I add one?
Talk about iconic, how about a nurse’s cap.
(incidentally, an awful lot of “naughty nurse” pictures come up if you search for “nurse’s hat”; makes finding a work-safe link darn difficult.)
Might as well. I’m going to follow your example with
armet for a knight in armor
An engineer’s cap.
Miner’s helmet with lamp.
A Fez a… monkey.
A fedora for a 1920s gangster.
Referee’s hat.
The Game Hat.
A deerstalker. Some equate this with detectives, but I’d rather correctly associate it with tweedy hunters.
In some rare photos, the pope is occasionally seen wearing something on his head, but it’s so small we can’t confirm or deny whether it’s a hat or the sun reflecting from a bald spot.
