Headgear, headwear or headdress is the name given to any element of clothing which is worn on one's head.

Caps and hats commonly worn today

Akubra

balmoral

baseball cap

batting helmet

beanie or skully and or visor beanie.

beret

bobble hat

bomber hat

boonie hat

Borsalino

bucket hat also fishing hat (UK) or Dixie Cup hat (US)