This is an incomplete list of headgear (that is, anything worn on the head), both modern and historical.
Beanie or skully and or visor beanie.
Boater (also basher, skimmer, cady, katie, somer, or sennit hat)
Bobble hat (tuque)
Bucket hat also fishing hat, ratting hat (UK) or Dixie Cup hat (US)
Bowler or Derby
Combination cap, also "service cap" or peaked cap
Cowboy hat, sometimes "Ten gallon hat"
Eight-point cap, also Gatsby cap, Newsboy cap