Find Godfather hats in all of the latest colors made of wool felt at AlligatorBoss.com. A Godfather hat is a mens dress hat that was originally called the Homburg. It is a dressier hat than your standard Fedora hat with its special grossgrain trim on the brim that has a slight roll to it. What also separates a Godfather is the crown which has only a center crease on the top and no pinch front. Originally they were worn by bankers and were known as a banker hat due to their dressier look. The Homburg hat was often the hat seen on both upper level business men and heads of state.