Cat brooch

A cat brooch or cat badge was a cat-shaped fashion accessory owned by the Doctor. He wore it on his left lapel, and touched it for good luck on occasion. (DW: The Twin Dilemma, Attack of the Cybermen)

Behind the scenes
One idea for the brooch originally was that it would change its expression to match the mood of the current situation, frightened cats when the Doctor was scared. Eventually this idea was dropped, though it would be subtly implemented in the illustrated webcast Real Time.

The production team settled for using different cat brooches in the following episodes. Many fans sent cat brooches to Colin Baker; he has claimed to have worn every single one. (DW: Attack of the Cybermen DVD Commentary)