Fedora

The Fourth Doctor sports a fedora. (TV: The Sun Makers)

A fedora was a hat.

Such a hat was part of the Fourth Doctor's outfit. (TV: Robot) He occasionally used it to cover his face to nap. (TV: Robot, The Androids of Tara)

The Seventh Doctor wore a paisley banded white fedora (PROSE: White Darkness) that he had had made especially for him. (PROSE: First Frontier)

When the Twelfth Doctor visited Las Vegas, he donned a fedora at Clara Oswald's insistence. (COMIC: Gangland)

The Dream Lord wears a chocolate brown fedora when he taunts the Eleventh Doctor, Amy Pond, and Rory Williams during the beginning of the Eknodine assault. (TV: Amy's Choice)

Diagoras wore a black fedora when he was getting recruits from Hooverville. (TV: Daleks in Manhattan)