Gough was born in Kuala Lumpur, Federated Malay States (now Malaysia) on 23 November 1916, the son of British parents Francis Berkeley Gough and Frances Atkins (née Bailie). Gough was educated at Rose Hill School, Tunbridge Wells, and at Durham School, he moved on to Wye Agricultural College which he left to go to the Old Vic. During World War II Gough was a conscientious objector, like his friend Frith Banbury, although he was obliged to serve in the Non-Combatant Corps, a member of 6 Northern Company, in Liverpool.
In 1948, Gough made his film debut in Blanche Fury and thereafter, appeared extensively on British television. In 1955, he portrayed one of the two murderers who kill the Duke of Clarence (John Gielgud), as well as the Princes in the Tower in Laurence Olivier's Richard III.
He became known for appearances in horror films including Dracula (1958), Horrors of the Black Museum (1959), Konga (1961), The Phantom of the Opera (1962), Black Zoo (1963), Trog (1970), The Corpse (1971), Horror Hospital (1973) and Norman J. Warren's stockbroker-Satanism debut Satan's Slave (1976). He also appeared in the comedy film Top Secret! (1984), alongside Val Kilmer (the latter's first feature film), with whom he would also work later in the Batman franchise.
Gough guest-starred in Doctor Who, as the villain in The Celestial Toymaker (1966) and also as Councillor Hedin in Arc of Infinity (1983). He also played the automation-obsessed, wheelchair-bound Dr. Armstrong in "The Cybernauts", one of the best remembered episodes of The Avengers (1965), returning the following season as the Russian spymaster Nutski in "The Correct Way to Kill". He was introduced in the first-season episode "Maximum Security" of Colditz as Major "Willi" Schaeffer, the alcoholic second-in-command of the Kommandant (Bernard Hepton). In the Ian Curteis television play Suez 1956 (1979), he portrayed Prime Minister Anthony Eden. In 1981, he was reunited with Laurence Olivier in Granada Television's Brideshead Revisited, portraying the doctor to Olivier's dying Lord Marchmain. Gough also appeared in The Citadel (1983) as Sir Jenner Halliday, in 1985's Out of Africa as Lord Delamere and as the fictional deposed KGB spymaster Andrei Zorin in Sleepers.
His later roles included Alfred Pennyworth for Tim Burton, including Batman (1989) and Batman Returns (1992). He also reprised his role as Alfred in the 1994 BBC radio adaptation of Batman: Knightfall and in Batman Forever (1995) and Batman & Robin (1997) for Joel Schumacher. Gough was one of two actors to have appeared in the four Batman films in the Burton/Schumacher series; the other actor was Pat Hingle (as Commissioner Gordon). Gough worked for Burton again in 1999's Sleepy Hollow and Corpse Bride. He also briefly reprised his Alfred role in six 2001 television commercials for the OnStar automobile tracking system, informing Batman of the system's installation in the Batmobile. Other commercial appearances famously included Gough as Alfred in a 1989 advertisement for Diet Coke.
Gough retired in 1999 after appearing in Burton's Sleepy Hollow. He would emerge from retirement twice more, both as a favor to Burton, to voice Elder Gutknecht in Corpse Bride and the Dodo in Alice in Wonderland.
Gough was married four times—one of his ex-wives is Anne Elizabeth Leon (born 1925). They married in 1950, their daughter Emma Frances was born in 1953 and they divorced in 1964. Another ex-wife is Doctor Who actress Anneke Wills, who portrayed the Doctor's companion Polly. Wills and Gough met at various times during her life —firstly during a theatre trip with her mother in 1952 — but they first met formally on the set of Candidate for Murder and the attraction was instant. Gough adopted Wills' daughter Polly and in 1965, their son Jasper was born.
Gough won Broadway's 1979 Tony Award as Best Actor (Featured Role – Play) for Bedroom Farce. He was also nominated in the same category in 1988 for Breaking the Code.
In 1957, he won a BAFTA TV Award and in 1971, was nominated for a BAFTA Film Award for his work in The Go-Between.
He was nominated for a Drama Desk Award Outstanding Featured Actor in a Play in 1979 for Bedroom Farce and again in 1988 for Breaking the Code.
Gough died on 17 March 2011 in London, England after a short battle with pancreatic cancer.
He was cremated, a memorial service was held, and his ashes were scattered at sea.
He was survived by his fourth wife Henrietta, daughter Emma and sons Simon (who is married to actress Sharon Gurney, the daughter of the Upstairs, Downstairs actress Rachel Gurney) and Jasper. Michael Keaton, his co-star in the first two theatrical Batman films, said that Gough was sweet and charming, and wrote, "To Mick – my butler, my confidant, my friend, my Alfred. I love you. God bless. Michael (Mr Wayne) Keaton."
Gough was added in In Memoriam at the 18th Screen Actors Guild Awards.