From my youth I recall the stereotypical depiction of a chinese person (maybe only chinese men) had them wearing a cone-shaped hat. The one that kinda looks like a carat ‘^’ from the side. Does anyone know what these were called? Can you tell me if they were really worn in China? Are they still worn in China?
In English, they are usually called “coolie hats”, which might be taken as pejorative, I suppose. I don’t know what they are actually called in Chinese. Yes, the style was, and is, actually worn throughout Asia.
I’ve heard numerous WWII (Pacific Theater) and Vietnam vets refer to them as “sampans”. IIRC, this is also the name of canoe-like boats, but they did talk about them as hats two or three times.
Tripler
I know, I’m ain’t too helpful, but that’s what I’ve heard 'em called.
I brought one back with me from Hong Kong. It had a frame inside that held the hat up off your head, and kept your head cool. Best thing I ever had for working in the yard, smart-assed neighbor comments aside. 
Only problem was finding another to fit my big head.
Peace,
mangeorge
Yup , I always called them coolie hats… 've seen them for sale in Hong Kong and Singapore. One day I will buy myself one.