Phrygian cap
look at the links below
cap and gown. the hat is called a mortarboard.
a leperchaun's hat :P
It's called a homburg hat
Its called a hat box
Check out the RELATED LINKS section for a link to Wikipedia regarding the Caps and its history.
According to Irish folklore, it's called a cocked hat.
A guardsman hat is called 'Bear Skin'
Its called a Tri-Corn Hat
a pilgrim hat is called a pilly hat
a hat is called 'un chapeau' (masc.) in French.
Look in the related links I will make for you below.