Fedora
From Tardis Wiki, the free Doctor Who reference
A Fedora is a felt hat most commonly worn by men. It can come in many different shapes and sizes along with individual names. Such a hat was part of the Fourth Doctor's outfit throughout his years, occasionaly using it to cover his face to nap. (DW: Robot, The Androids of Tara) However, during the middle of his tenure, he prefered to go without it unless the weather called for a hat.
