From Homestar Runner Wiki
Headgear is any type of covering for the head, such as a hat or helmet. Every main character and a lot of the secondary characters have worn some type of headgear at various times, the styles of which vary greatly. Homestar Runner wears a propeller cap, Homsar wears a bowler, The King of Town wears a crown, and Coach Z wears a backwards baseball cap. In the photobooth in Strong Bad's Cool Game for Attractive People, Strong Bad can wear a wide selection of headgear. In Where My Hat Is At?, Homestar loses his hat and later finds it in his refrigerator between the milk and the cold ones. The Broternal Order of Different Helmets wear a wide variety of helmets. Strong Bad's painting of a guy with a big knife wears a headband a lot like Rambo's.
In addition to regular headgear, some unusual things can be found: For example, the members of the Homestarmy wear orange plastic bowls on their heads, and The Deleteheads wear delete keys. Marzipan wears a fake afro in the Joy of Painting.
Marzipan does not usually wear a hat, but she wears a bobble which could be considered headgear.