A tricorn was a type of hat.
Worn by the Doctor
The Second Doctor once wore a British Army tricorn as a disguise. (TV: The Highlanders)
One of the Doctor's incarnations predating the First Doctor wore a tricorn. (TV: The Brain of Morbius) The Eighth Doctor later found his old tricorn in the TARDIS secondary control room, reminiscing that it had been "ages" since he'd worn it. (TV: The Brain of Morbius)
Companions
Amy Pond wore a black tricorn when using a cutlass to save the Eleventh Doctor and Rory from the pirates of the Fancy. (TV: The Curse of the Black Spot)
Worn by Others
Henry Avery, a leading pirate, wore a black tricorn. (TV: The Curse of the Black Spot, A Good Man Goes to War)
Avatar wore a tricorn hat. (PROSE: Of the City of the Saved...)