Gough was born in Malaysia and made his film debut in the 1948 movie Blanche Fury. He went on to appear in many British television shows, including the long-running series Doctor Who. He married his costar from the series, Anneke Wills, in 1962. They later divorced in 1979.
Gough also appeared in many British horror films such as The Phantom of Opera (1962), The Corpse (1970) and Dracula (1985). In 1979, Gough won a Tony Award for Best Actor for his role in Bedroom Farce.
Gough began his working relationship with director Tim Burton on the 1989 film Batman. He reprised his role as Alfred Pennyworth, Bruce Wayne's butler and father figure, in Batman Returns (1992). Gough also played Alfred in the 1994 BBC radio adaptation Batman: Knightfall and in Joel Schumacher's films, Batman Forever (1995) and Batman & Robin (1997). He worked with Burton again in Sleepy Hollow (1999), Corpse Bride (2005) and Alice in Wonderland (2010).
Gough is survived by his fourth wife, Henrietta.