It's a scene etched into our collective unconscious. The smiling couple waving to crowds from a black open-top limousine. Bright green grass. Her bright-pink suit and hat. Then something seems to catch his throat. She leans over to him. His head snaps back and forth violently. She rises out of her seat and reaches out across the boot in horror. The car speeds up and drives off.

Except something's not right. That's not Jackie Kennedy in the pink suit; it's a man in drag. And the president doesn't seem to be hurt after all. In fact, they've driven right round Dealey Plaza and the whole thing is happening again. This isn't Abraham Zapruder's infamous home movie; it's actually The Eternal Frame, a brazenly irreverent reenactment of the Kennedy assassination, or more accurately, a reenactment of the Zapruder film itself. It was made in November 1975 by two San Francisco-based art collectives, Ant Farm and TR Uthco. Just before the "shooting", the actor playing JFK makes a television address. "I am in reality only another link in that chain of pictures which makes up the sum total of information accessible to us all as Americans," he says, in an exaggeratedly thick Boston accent.

"It was, of course, in bad taste," says Chip Lord, Ant Farm's co-founder, now a film professor at the University of California Santa Cruz. "Just to do anything other than show reverence towards the Kennedy family and the myth was obviously a taboo in American cultural life. So that became an attraction of the project. I think we felt there might be some essential truth in going to Dallas and re-performing the event."

They didn't have any official permits, Lord recalls. They just turned up and started shooting early one Sunday morning. When no one stopped them, they went round and did it again, and again – maybe 20 times. A crowd of tourists formed to watch. Many of them assumed it was an official event. In the film, one woman sheds tears and calls it "a beautiful reenactment", which it clearly isn't.

JFK has been dying again and again ever since, particularly in the movies. The echoes of his assassination still resound through cinema. The post-JFK golden age of Hollywood conspiracy thrillers has been well chronicled, but what has arguably had a deeper impact is the Zapruder film itself. From the moment it recorded Kennedy's life horrifically cut short, it took on a life of its own. It is technically a short documentary: just 26 seconds long, 486 silent, colour, 8mm frames. It is also an official piece of evidence, a historical record, an art object, a genuine snuff movie. Some have called it the foundation stone of citizen journalism – a harbinger of the current YouTube era, where anyone with a camera can create something of global broadcast value. To some, as well as JFK's death, the Zapruder film represents the death of cinematic truth itself.

None of this was anywhere near Zapruder's mind when he strolled out to Dealey Plaza on his lunch break to record Kennedy's drive-past. Zapruder had actually left his camera at home that day. An assistant in his dress factory persuaded him to go back and get it. Within hours of the assassination, Zapruder had given copies of his movie to two men, thus setting it off on divergent but intersecting paths. The first was Secret Service agent Forrest Sorrels, who requested it for official investigatory use. The second man was Richard Stolley, an editor at Life magazine, who won the media bidding war for the movie. Zapruder sold it to Life for $150,000, with the promise that they never publish frame 313: the fatal shot itself.

The world knew about the existence of the Zapruder film almost immediately. CBS presenter Dan Rather described its contents (inaccurately) on television, two days after the assassination. Life printed still images from it in its commemorative issue a week later, and would go on to print images over the coming decade. But mainstream audiences would not get to see the entire, unedited film until March 1975, when it was shown on late-night TV. That was a few months before The Eternal Frame's reenactment, but, by then, Ant Farm and many others had already obtained bootleg copies of the film. Lord got his through a contact with "a conspiracy-type network," he says. "It was a 16mm copy. The colour was almost completely washed out." That didn't stop a local TV station asking if they could borrow it to broadcast.

By that time, the film had already seeped into popular culture. The Kennedys were rapidly co-opted into Andy Warhol's lexicon, since they ticked the boxes for both media celebrity and violent crime. Many of Warhol's iconic images of the couple were based on photos from Life magazine. Like Ant Farm, he was commenting on the media portrayal of the event. "What bothered me was the way television and radio were programming everybody to feel so sad," he said at the time. "It seemed like no matter how hard you tried, you couldn't get away from the thing." Warhol turned Zapruder himself for his 1966 film Since – an unfinished, amateurish reconstruction using his regular Factory "superstars". In 1967, film artist Bruce Conner incorporated the Zapruder film in his influential Report, a stirring montage of news footage and voiceovers from the day of the assassination. Then John Waters restaged Zapruder in his very first film, 1968's Eat Your Make Up, on his parents' lawn, with Divine as Jackie Kennedy. Now the Zapruder film is out there in the pop-cultural ether, reproduced and referenced in movies (from Kentucky Fried Movie to In The Line of Fire to Watchmen), sitcoms (Seinfeld, Family Guy) and music videos (Lana Del Rey's National Anthem).

But that other path the Zapruder film took, via the copies he handed to the Secret Service, created a parallel history. From Sorrels the film found its way to the investigating Warren Commission the following year. However, the commission's printed reproductions of it omitted some frames and switched around others, planting seeds of suspicion. Over the course of subsequent investigations of the Kennedy assassination, official and unofficial, the Zapruder film somehow became evidence of a cover-up. It still is today. A simple internet search throws up dozens of analyses of the footage, explaining why it is a fake, how it has been doctored, why it doesn't match other official accounts, why there was another shooter – you name it.

Billy Bob Thornton in Parkland.

"You might think it would close down conspiracy theories but it opens them up," says Dr Clare Birchall from the Institute of North American Studies at King's College London, who has written extensively on conspiracy culture. The fact that the Zapruder film "proves" so many conflicting versions of events says something about the inherent instability of film as factual record, and the gap between film and experience, she suggests. "The camera 'never lies', and yet it is precisely that which allows one to lie. Visual evidence is eminently interpretable. In that sense it already contains the possibilities of conspiracy theory."

You can see the same process in modern-day events such as 9/11, Birchall continues, where the same images have been used to support innumerable theories. "But in terms of disputed visual evidence, the Zapruder film is the classic. It's seen as the motherlode of conspiracy theory. The theories that draw in everything, from the Illuminati to the New World Order, always have JFK in there at some point." Is cinema any different? What is a movie if not a selection of moving images arranged into a persuasive narrative? No wonder so many film-makers have been drawn to the subject. Within that golden age of Hollywood conspiracy thrillers, a few addressed the ambiguity of media directly – Antonioni's Blow-Up and Coppola's The Conversation. But in later years has come a new breed of film-maker committed to cracking the JFK mystery themselves. Prime suspect: Oliver Stone, and his 1991 movie JFK, in which district attorney Jim Garrison, played by Kevin Costner, pieces together a vast conspiracy involving Lyndon Johnson, the CIA, the mafia, the military-industrial complex, the gay community, possibly the Dallas Cowboys – it gets confusing. Ostensibly based on fact, it uses repeated playings of the Zapruder film to give credence to Garrison's on-screen argument, but in terms of historical accuracy, it's as flawed and contestable as the crackpot YouTube theories.

Still, Stone's JFK struck a chord with an American public who felt they still weren't getting the truth. Its success prompted the US government to collect and make public all the government records relating to the assassination to prove there was no conspiracy. Those records included the Zapruder film: the US government took possession of the film under the 1992 law known as the JFK Act, and in 1999 a special arbitration panel awarded $16m plus interest to the Zapruder family as compensation, after which they donated the copyright to the Sixth Floor Museum at Dealey Plaza. The asking price for use of it in a movie, such as JFK, is now $80,000.

Stone hasn't been the only one drawn back to Dealey Plaza. In 2011, Oscar-winning documentarian Errol Morris made a short film focusing on the "Umbrella Man" – a background figure, caught in the Zapruder film incongruously holding an open black umbrella that sunny day. Was it a signal? A concealed weapon? Morris's film closes the case (no spoilers here), only for another esteemed film-maker, Alex Cox, to reopen it. Cox posted a YouTube response effectively dismissing Morris's film. He's something of a JFK nut, it turns out. In another YouTube short, Cox questions the authenticity of the Zapruder film itself. He has recently published a book on JFK and Lee Harvey Oswald. Doing a considerably more thorough job is Irish film-maker Shane O'Sullivan, whose new documentary, Killing Oswald, which sifts through the paperwork made public after Stone's JFK, and raises compelling new questions about the whole affair.

And finally we have Parkland, a new big-budget dramatisation of events, produced by Tom Hanks. Centred on the hospital that treated both Kennedy and Oswald after they were shot, it includes all the now-familiar suspects: agent Sorrels (played by Billy Bob Thornton), the Dallas police, Oswald and his family, and here's our man Zapruder, played by the eminently sympathetic Paul Giamatti. Parkland almost functions as a Zapruder "making of". Rather than restaging the assassination yet again, it homes in on Zapruder's face during those moments, registering his shock as he films. Similarly, the only time we see Zapruder's film, it's reflected in the spectacles of Zapruder himself. Giamatti found the experience overwhelming, says Parkland's writer and director, Peter Landesman. "He had a little nervous breakdown before he started. He's playing Zapruder, in Zapruder's clothes, where Zapruder was in Dealey Plaza. It was a very weird out-of-body experience. He enjoyed it but it was a very freaky thing."

Landesman, a former journalist, doesn't indulge in any conspiracy theorising. "There's no doubt where the bullets came from unless you really want to believe in Santa Claus." Instead, Parkland restores some humanity to events numbed by 50 years of mediation and repetition, putting us in the emergency room as doctors frantically try to revive the dying president, as Jackie hands them a piece of her husband's skull she's still clutching.

The film also restores some humanity to Zapruder himself. Landesman had prolonged conversations with his family to obtain their permission, and he feels great sympathy for the man. Zapruder was the embodiment of the American dream: a Russian Jewish immigrant who worked hard to integrate and to make his fortune. Some accused him of greed for demanding money for the film, but Landesman (who also stumped up his US$80,000 for the rights) is more forgiving: "He was smart enough to know what was going to happen. He wanted some kind of compensation for what he knew was the end of his life as he knew it, but also it was the crushing of his American patriotism. Immigrants are converts and converts make the most vociferous ideologues. He was a flag-waving patriot, so to have his president have his head blown off right in front of him was a big deal."

Zapruder was haunted by the assassination for the rest of his life. He testified at both the Warren Commission hearings and the Clay Shaw trial in 1969. He wept on both occasions. "I have seen it so many times," he told the Warren Commission, having been effectively forced by law to watch his film again. "In fact, I used to have nightmares. The thing would come every night – I wake up and see this." He died of cancer in 1970. According to his family, after 22 November 1963, he never looked through a camera lens again.

• This article was corrected on 6 December 2013. The earlier version said "the [Zapruder] family sold the film to the government for $16m, though they still retain the copyright." In fact the family no longer retain the copyright, and therefore no longer license or receive payment for its use. The article has also been amended to clarify the process by which the family were compensated after the government took possession of the film.