Hurt was born in Chesterfield, Derbyshire, the son of Phyllis (née Massey), an amateur actress and engineer, and Arnould Herbert Hurt, a mathematician who became an Anglican clergyman and served as vicar of Shirebrook. Hurt's father was also a vicar at St John's Church in Sunderland. In 1937, he moved his family to Derbyshire, where he became Perpetual Curate of Holy Trinity Church. When Hurt was five, his father became the vicar of St. Stephen's Church in Woodville, Derbyshire, and remained there until 1952.
In 1945, Hurt's father founded 1st Woodville (St. Stephen's) Scout Group, which is still going today. Hurt had a strict upbringing; the family lived opposite a cinema, but he was not allowed to see films there. He was also not permitted to mix with local children because his parents saw them as "too common".
At the age of eight, Hurt was sent to the Anglican St Michael's Preparatory School in Otford, Kent, where he eventually developed his passion for acting. He decided he wanted to become an actor, and his first role was that of a girl in a school production of The Bluebird (L'Oiseau Bleu) by Maurice Maeterlinck. While he was a pupil at the school, he was abused by Donald Cormack (now deceased), then Senior Master of the school and later Head Teacher (until his retirement in 1981). Hurt described how Cormack would remove his two false front teeth and put his tongue in the boys' mouths, and how he would rub their faces with his stubble. Hurt said that the experience affected him hugely.
Hurt's father moved to Old Clee Church in Grimsby, North East Lincolnshire. Hurt (then aged 12) became a boarder at Christ's Hospital School (then a grammar school) in Lincoln, because he had failed the entrance exam for admission to his brother's school. Hurt often accompanied his mother to Cleethorpes Repertory Theatre, but his parents disliked his acting ambitions and encouraged him to become an art teacher instead. His headmaster, Mr. Franklin, laughed when Hurt told him he wanted to be an actor, telling him that he "wouldn't stand a chance in the profession". Aged 17, Hurt enrolled in Grimsby Art School (now the East Coast School of Art & Design), where he studied art.
In 1959, Hurt won a scholarship allowing him to study for an Art Teacher's Diploma (ATD) at Saint Martin's School of Art in London. Despite the scholarship, paying for his studies was financially difficult, so he persuaded some of his friends to pose nude and sold the portraits. In 1960, he won a scholarship to RADA, where he trained for two years. He was then cast in small roles on television.
Hurt's first film was The Wild and the Willing (1962), but his first major role was as Richard Rich in A Man for All Seasons (1966). In 1971 he played Timothy Evans, who was hanged for murders probably committed by his landlord Reg Christie, in 10 Rillington Place, earning him his first BAFTA nomination for Best Supporting Actor. His portrayal of Quentin Crisp in the 1975 TV play The Naked Civil Servant gave him prominence and earned him the British Academy Television Award for Best Actor. The following year, Hurt played the Roman emperor Caligula in the BBC drama serial, I, Claudius. In 1978, he appeared in Midnight Express, for which he won a Golden Globe and a BAFTA and was nominated for an Academy Award for Best Supporting Actor (the latter of which he lost to Christopher Walken for his performance in The Deer Hunter). Hurt voiced Hazel, the heroic rabbit leader of his warren in the film adaptation of Watership Down and later played the major villain, General Woundwort, in the animated television series version.
His roles at the end of the 1970s and the beginning of the 1980s included Kane, the memorable first victim of the title creature in the film Alien (a role which he reprised as a parody in Spaceballs); would-be art school radical Scrawdyke in Little Malcolm; and "John" Merrick in the Joseph Merrick biography The Elephant Man, for which he won another BAFTA and was nominated for a Golden Globe and an Academy Award for Best Actor. In 1978, he lent his voice to Ralph Bakshi's animated film adaptation of Lord of the Rings, playing the role of Aragorn. He also had a starring role in Sam Peckinpah's critically panned but moderately successful final film, The Osterman Weekend (1983). Also in 1983 he starred as the Fool opposite Laurence Olivier's King in King Lear. Hurt also appeared as Raskolnikov in the 1979 BBC TV mini-series adaptation of Crime and Punishment.
Hurt played Winston Smith in the 1984 adaptation of the novel Nineteen Eighty-Four. In 1985, he starred in Disney's The Black Cauldron, voicing the film's main antagonist, the Horned King. In 1986, Hurt provided the voiceover for AIDS: Iceberg / Tombstone, a public information film warning of the dangers of AIDS. In 1988 he played the title role, the on-screen narrator, in Jim Henson's The StoryTeller TV series. He had a memorable supporting role as "Bird" O'Donnell in Jim Sheridan's 1990 film The Field, which garnered him another BAFTA nomination. In 1997, Hurt played the reclusive tycoon S.R. Hadden in Contact. In 2001, he played Mr. Ollivander, the wand-maker, in the first Harry Potter film, Harry Potter and the Philosopher's Stone. He returned for the adaptation of Harry Potter and the Goblet of Fire, though his scenes in that film were cut. He also returned for Harry Potter and the Deathly Hallows – Part 1 and Part 2. In 1999, Hurt provided narration on the British musical group Art of Noise's concept album The Seduction of Claude Debussy. During this time, he narrated a four-part series on the Universe which was released on DVD in 1999. In the 2006 film V for Vendetta he played the role of Adam Sutler, leader of the Norsefire fascist dictatorship. In May 2008, he appeared in Steven Spielberg's Indiana Jones and the Kingdom of the Crystal Skull as Harold Oxley. He is also the voice of The Great Dragon Kilgharrah, who aids the young warlock Merlin as he protects the future king Arthur, in the BBC television series Merlin.
In 2008, 33 years after The Naked Civil Servant, Hurt reprised the role of Quentin Crisp in An Englishman in New York. This film depicts Crisp's later years in New York.
In June 2009, Hurt played the on-screen Big Brother for Paper Zoo Theatre Company's production of Orwell's Nineteen Eighty-Four. The theatre production premiered at the National Media Museum, in Bradford and will be touring during early 2010. Hurt said, "I think Paper Zoo thought it would be quite ironic to have the person who played Winston having risen in the party. From the Chestnut Tree Cafe, he's managed to get his wits together again, now understanding that 2 and 2 make 5, and becomes Big Brother. So it tickled my fancy, and of course I looked up Paper Zoo, and they seem to me to be the sort of company that’s essential in the country as we know it, and doing a lot of really good stuff."
At the 65th British Academy Film Awards Hurt won the award for Outstanding British Contribution to Cinema.
In 2013, Hurt appeared in the Doctor Who 50th anniversary episode "The Day of the Doctor", as a 'forgotten' incarnation of the Doctor, known as the War Doctor.
Hurt is due to appear alongside Ben Kingsley in a film entitled Broken Dream, to be directed by Neil Jordan.