Matt Smith really doesn't want to be typecast as the guy from Doctor Who any more. That's why he's starring as Patrick Bateman in American Psycho – a musical stage version of American Psycho, in fact. As professional handbrake turns go, it's pretty drastic. But he isn't the first. History is littered with actors who've been pushed to extreme measures to break out of their typecasting straitjackets. Here are some of the best.

Hugh Grant

It's a shame nobody really saw Cloud Atlas, because it contained the largest assembly of actors performing against type in modern cinema. Lovely, funny Tom Hanks played a sort of post-apocalyptic caveman. Halle Berry was a male Korean dentist. But most startling of all, Hugh Grant broke his 20-year run of playing the same bumbling, ineffectual romantic lead to become a bald, facially tattooed cannibal tribesman. It was as far from Music & Lyrics as you can get, so no complaints.

Mariah Carey

Mariah Carey's first film lead won her a best actress award. But the film was Glitter (2001), and the award was a Golden Raspberry. Then Lee Daniels came to her rescue in 2009, scraped off the slap, stripped away the sequins, encouraged a light moustache and cast her as a social worker in Precious (for which she won proper awards).

Lenny Henry

In 2009, one actor's turn as Othello was described by one critic as "one of the most astonishing debuts in Shakespeare I have ever seen". The actor in question was Lenny Henry, a man who'd spent much of his career shouting the word "Katanga!" and throwing custard pies at Chris Tarrant while dressed as Trevor McDonald. It would have been a perfect transformation were it not for his subsequent decision to channel all that classical stage experience into reciting poems about budget hotels on TV.

Daniel Radcliffe

Radcliffe's career has had two distinct halves. There was the half where he was made to say "A wuh-wizard?" on a green-screen stage every day for a decade, then the half where he disrobed for a paying audience and stabbed a horse in the eye. When he starred in Equus, he planted a flag in the ground: the rest of his life would be spent distancing himself from Potter as violently as possible. The fact that he went on to make Young Doctor's Notebook (morphine addict) and Kill Your Darlings (nudity and drug-taking) is proof. Radcliffe is currently filming a remake of Frankenstein, playing Igor.

Pauline Quirke

Quirke could have had a perfectly comfortable career playing downbeat housewives in mainstream sitcoms. But then she made The Sculptress, an incredibly distressing BBC miniseries about a woman convicted of murdering her family and arranging their limbs into abstract shapes. Suddenly she was a dramatic actor. Sure, she wouldn't be able to make any more sitcoms, because the sight of her cold, dead eyes made everyone involuntarily burst into tears and run away, but that was probably the point (see also: Broadchurch).

Liam Neeson

His Michael Collins was a triumph. His Oskar Schindler was perfect. Liam Neeson was the actor's actor, picking up Oscar and Golden Globe nominations wherever he went. And then he junked it all by starring in Taken – an action film about a man who tells another man he's going to find him and kill him, and then finds him and kills him. Since then, Liam Neeson has become Hollywood's go-to, vaguely geriatric vigilante. He won't win any awards for this new direction, but at least nobody's going to start a fight with him.

Kaya Scodelario

Scodelario became famous as Effy in Skins, the TV show written by and starring young people doing young people things: bad sex, OK drugs, sarcastic banter. She then contrasted it with the role of Cathy in Andrea Arnold's adaptation of Wuthering Heights – though kept her yoof credentials by admitting she hadn't read it.

Sean Connery

It's hard enough to convince anyone you're not James Bond any more, which might explain why Roger Moore hasn't really bothered. But for Sean Connery it must have been impossible. "If only there was a role," he must have thought, "where I could grow a ponytail and moustache and run around an alien planet in a sort of proto-Borat mankini." Luckily for him, the script for John Boorman's Zardoz – which required him to do exactly that – landed on his desk shortly afterwards.

Mark Wahlberg

As the lead singer of Marky Mark and the Funky Bunch, Wahlberg's lifestyle was the envy of the world. He travelled the globe, swamped with adoring fans, never wearing a sweater and only rarely a belt. But he wanted more. He wanted people to take him seriously. So, just like that, he became an actor. Mark Wahlberg the rapper was dead; Mark Wahlberg the man who makes violent films you might watch on an aeroplane was king. He would eventually make another major career turn, into a man who made films that people did want to see, but that would be years away.

Charlize Theron

Theron had an enviable acting career on the go, starring in films by Robert Redford and Woody Allen, but it wasn't until she did Monster that she won an award. Why? Because until then she was seen as nothing more than eye-candy. But in Monster, she fattened up and stopped washing. It was a transformation, and all the vindication she needed. She, and every other film actress brave enough to wear the sort of clothes that normal people wear, deserve our gratitude.

Helena Bonham Carter

Helena Bonham Carter was once the definitive porcelain face of Merchant Ivory – so much so that it was genuinely unsettling to see her out of period dress. But then in 1999 she starred in Fight Club as a damaged chain-smoker who may or may not be a secondary figment of the protagonist's imagination. The role immediately cut her free and allowed her to do anything she wanted, which turned out to be making loads of films with Tim Burton and Johnny Depp.

Hugh Laurie

Everyone's favourite gormless sidekick stuck firmly to the laughs, whether on small screen (Blackadder, A Bit of Fry and Laurie) or big (Peter's Friends, 101 Dalmatians, Stuart Little). But then Hollywood came a-calling, and even after Dr House laid down his cane for good in 2012, Laurie's movie choices have tended to be as blue as his music.