A Clockwork Orange

Near future England:  Teenage gang leader Alex (played by Malcolm McDowell) leads his three friends (or "droogs") on nightly rampages of theft and savage violence against whoever is unlucky enough to encounter them.  Tiring of Alex's arrogance, his friends set him up to be arrested after their latest attack goes fatally wrong.  Alex is convicted and sentenced to fourteen years in prison.  After two years inside, Alex is submitted to an experimental treatment called the "Ludovico Technique" which is intended to cure criminality by making the subject unable to act violently.  Alex is released after the treatment and soon finds that where he was once the predator, he is now the prey.

Released in 1971, written and directed by Stanley Kubrick, and based on the 1962 novel by Anthony Burgess, this is hugely controversial film is now acclaimed as a modern classic.  It is still a shocking film, in fact I would say that it would probably not get made today. because it would just be too problematic.  Not necessarily because of the on-screen violence, which is heavily stylised and more shadowplay than graphic blood and gore, but because we are invited to like and sympathise with a  brutal, unrepentant rapist and murderer.  The entire film is shown through Alex's eyes, and he breaks the fourth wall with his voice-over narration (addressing the audience directly as "my brothers and only friends").  The first part of the film, depicting Alex's crimes is heavily stylised, whereas the latter part of the film, where Alex becomes the victim, the violence is much more realistically depicted thereby inviting the audience to enjoy Alex's rampages at a distance, but to sympathise with his own sufferings.  Which is, of course, how Alex would see it.  Also there is the towering performance of Malcolm McDowell as Alex, alternately threatening and innocent, it is a career best performance, and he is in pretty much every scene of the film. 
The film is relatively faithful to the novel, although it discards the final chapter of the original, British version of the book.  There are some odd elements in regards to the book, in which Alex's age is stated as being fourteen.  Malcolm McDowell was in his late twenties when he made the film, and yet he is constantly referred to as a child, despite being clearly an adult.
The film depicts a very seventies future, and it really is a product of it's time and place, it feels more like an alternate early seventies than a futuristic piece.  The novel was written in an invented slang called "Nadsat" and this is memorably retained in the film, although toned down.  Burgess invented nadsat because he felt that if he wrote it in then-current slang then novel would feel dated as soon as it was published, and he was right.
The film was famously withdrawn from release in Britain by Kubrick himself and was not legally available there until after his death.
It is still a troubling, shocking and powerful experience.