Coulrophobia

Coulrophobia is the irrational fear of clowns. Luke Smith noted this psychological disorder by its proper name when a clown began appearing to the students at his school. Sarah Jane Smith was a known sufferer from an early age. She had been introduced to the phobia by a toy clown that used to hang near her bed. She claimed that its unnatural gaze used to terrify her at night. As an adult, she discovered that the toy had, in fact, been manipulated by the Pied Piper to instill this fear in her.

Luke alleged that Johnny Depp also suffered from the phobia, according to Heat magizine. (SJA: The Day of the Clown)

Ace was scared of clowns, as she found out on Segonax. However it is unclear whether she had coulrophobia, or merely an aversion to them. (DW: The Greatest Show in the Galaxy)

Toshiko Sato also had coulrophobia. She channelled this fear to create a monster clown to fight against the creations of Gareth Portland. (TWN: Pack Animals)

Darius Pike had coulrophobia as well. On his sixth birthday, his father hired a clown called Mr. Floppy Fun Pants to come to his party, with the young Darius being terrified at his antics. He later said it was the worst birthday party he ever had in his life. This fear was exploited by the Bodach who gave him a dream where he was locked in Mariah, his antique car, with clowns. (K9TV: Dreameaters)

Behind the scenes
David Tennant has admitted to suffering from the phobia, citing a sequence in The Deadly Assassin as a moment when he was "proper scared" by Doctor Who as a young viewer.