My cap was not fake fur! It was genuine rabbit fur!
My dad grew up in ranch country. He said that you should never hire a cowboy who rolled his own cigarettes or who wore a straw hat. “If he wasn’t trying to roll a cigarette in the wind, he was always chasing that @#$% hat.”
Miller’s Crossing has another hat, apparently quite a tall hat, that is never seen, but engenders quite a bit of discussion among the film’s characters. In particular, who has it, and who is attempting to give it to whom.
Also, from the Disc, Rincewind’s hat says “wizard” like no other. Specifically, is says “WIZZARD”
I’m assuming your tounge is firmly planted in your cheek on that one. For those not in the Know he is refering to teh saying “giving him the high hat” or brushing someone off.
But Miller’s crossing has a hell of a lot of hat/headpiece imagry.
“Rug” Daniels missing rug
Tom Figurativly chasing after his hat (Going to Vernas to get it back after he lost it in a poker game.)
Tictac tossing his away before he beats on Tom.
Everytime Leo is shown as week he has his hat in hand.
Bernie is first seen with his bowler on his foot. It seems too small for his head… even smaller when it is found in “drop” Daniels home.
The closing shot of Tom staring up under the brim of his hat.
Lot’s o’ hats… proabaly more examples I have missed.
The Archchancellor’s Hat in Sourcery by Terry Pratchett fights a magical war.
The Moment of the Magician by Alan Dean Foster, a low class stage magician in transferred to a fantasy world and can work real magic, including various tricks with his hat, like summoning things from it. When pushed to his limit, he manages to summon Death itself from the hat - which promptly takes him.
If crowns count, there are various important fictional ones.
The Crown of Alkyra in Shadow Magic by Patricia Wrede is the lost symbol of kingship, and can be only be worn by the rightful ruler ( because it fries anybody else who tries ). It’s recovered by the story’s heroine, who uses it to help stop an invading army, defeat it’s Shadow-Born leaders and becomes Queen.
The search for the lost crown of Thalasia was a central point in David Edding’s The Ruby Knight.