A bowler hat was a type of domed hat worn by the working class during the late 19th century. It was also commonly worn on Sigma Iotia II during the 23rd century.
Joe Falling Hawk, a Native American card shark who lived in San Francisco wore a bowler hat. Data later won the hat in a poker hand. (TNG: "Time's Arrow")
This type of hat was identified in the episode's script.
Numerous Iotian bosses, including Tepo, all wore bowler hats. (TOS: "A Piece of the Action")
Geordi La Forge wore a bowler as part of his role as John H. Watson in Data's Sherlock Holmes Program 3A scenario. (TNG: "Elementary, Dear Data")
This type of hat was identified in the episode's script.
Joe Falling Hawk wearing a bowler hat
Geordi La Forge as John H. Watson wearing a bowler hat
Tepo wearing a bowler hat
Carl wearing a bowler hat