1. The moon landings were faked
What's the theory? There are serious inconsistencies in the footage of Neil Armstrong as he makes that giant leap for mankind. These glitches and errors reveal that the footage was in fact cooked up in a television studio somewhere to fool a gullible world. First, the moon's surface is, we are told, very dry and dusty. If that is the case, why do Armstrong's footprints show up so boldly? Second, there is no wind in space. So why does the US flag planted in the surface of the (alleged) moon flap and flutter like there is a breeze? Surely it would just hang there inert, wouldn't it? Third, why are there no stars in the sky although they would be plainly visible in that atmosphere? Fourth, all the pictures of the moon landing, supposedly taken at different points along a five-kilometre stretch, have exactly the same backdrop. How is that possible? Could it be that Nasa just couldn't afford to splash out on very good sets?
Who says? The theory originated with Bill Kaysing, a man who used to work as a writer/librarian for Rocketdyne, a company involved in the construction of the Apollo lunar landers. He still presents himself as an expert in the field - even though he left the company in 1963, well before most of the Apollo work, and his job was unscientific and rather tenuously linked to Nasa. But Kaysing claims to be a whistle-blower, and his theories found fertile ground in an ultra-sceptical, post-Watergate America.
How likely is it? Well, Richard Nixon was president at the time, so anything is possible. But Nasa claims that most of the purported flaws in the footage are caused by the simple fact that 1960s film cameras were not especially high-quality. So, for example, although the stars would have been visible to the naked eye, they are absent from the pictures of the landings because they could not be captured by the primitive camera lens that was used. Almost all independent analyses of the evidence conclude that Nasa makes a persuasive case. And, if there really had been such a huge conspiracy - which would have involved an enormous number of people - would nobody but Kaysing have come forward in the past 40 years?
2. The Russian leader Vladimir Putin planted bombs in civilian areas in 1999, in the run-up to the presidential election, to whip up hysteria about Chechen terrorism and secure his victory
What's the theory? In September 1999, more than 300 people died when four apartment buildings, two in Moscow and two in other Russian cities, were blown up. The Russian people panicked; the new (and as yet unelected) prime minister, Vladimir Putin, immediately blamed Chechen terrorists. In fact, the bombings were carried out by the FSB (the Russian secret services) to guarantee Putin's victory. They wanted to create a sense of crisis so that they could vindicate his ultra-hardline policy on Chechnya, reverse his declining popularity and secure his election. It worked. In March 2000, he won by a landslide.
The conspiracy was revealed after a third block of flats that was targeted for bombing on the same day in Ryazan, 100 miles south of Moscow, was saved when an engineer spotted both the bomb and three suspicious-looking individuals nearby. The police arrested the men, who turned out to be Russian secret service agents, and so were released. They claimed it had been a "training exercise", but they had been using a real bomb - this in a building with more than 250 residents.
Who says? A highly respected team of journalists investigated the affair for Channel 4's Dispatches programme. They asked pointedly: "Was Vladimir Putin . . . implicated in an atrocious conspiracy to justify the terrible Chechen war? Were the Moscow bombings . . . part of the bloody price that had to be paid to get him elected to the Kremlin?" This has now been backed up by several leading Russian figures, including the media mogul Boris Berezovsky, now in self-imposed exile.
How likely is it? It sounds far-fetched at first, but remember that the FSB is simply the renamed KGB, whose raison d'etre for decades was essentially institutional terror in the service of the government. Putin is himself an ex-KGB man, and he has twice blocked, through the Duma, any independent investigation into the bombings. No evidence of Chechen involvement has ever been forthcoming, and the Chechen groups have claimed that they were not responsible - although they admit to other acts of violence. The Ryazan "training exercise" excuse is preposterous. It does seem to suggest that the Russian secret services were caught red-handed.
3. Bill and Hillary Clinton had their close friend and White House staffer Vince Foster murdered, and the death scene was fixed to look like a suicide
What's the theory? On 20 July 1993, Vince Foster was found in his car in a forest in Washington, DC. He had suffered a fatal gunshot wound. Foster was central to the Whitewater land deal that was turning into a major scandal for the president - and he knew where the Clintons' bodies were buried. He became a danger to Bill and Hill, so they ordered an assassin to shoot him.
Who says? The New York Times's resident right-winger, William Safire, questioned the suicide verdict and the USA's most popular radio host, Rush Limbaugh, began to promote the idea that it was a murder. Now there are more than 300 websites dedicated to the "conspiracy", which is still propagated by a number of hard-right senators and fanatical US militia groups.
How likely is it? Bill Clinton does have a record of killing people for political ends. During the 1992 election campaign, he returned to the governor's mansion in Arkansas personally to authorise the execution of a mentally handicapped black man. Following the 1998 al-Qaeda attack on the US embassy in Nairobi, he ordered an immediate retaliatory bombing against a harmless pharmaceuticals factory in Sudan. Noam Chomsky has calculated that 10,000 people died because they were deprived of medication manufactured at the factory. But the death of Vince Foster was thoroughly investigated in the 1990s. Even Clinton's nemesis, the special prosecutor Kenneth Starr, concluded after months of investigation that it was indeed a suicide (Foster had a history of depression) and that there was no connection between the death and the First Family.
4. Diana, Princess of Wales, was murdered
What's the theory? Take your pick. There is no one overarching theory explaining either the mechanics of the "murder", or the motives for it. Some of the theories concentrate on Henri Paul, the Ritz chauffeur who was driving the car in which Diana died. The autopsy on his body revealed that he had extremely high levels of alcohol and medication in his bloodstream, so most conspiracists claim that he was drugged in order to cause a deadly accident. Others speculate that Paul was involved with secret services work in Paris and had been a "contact" for MI6. Some even claim that he was a "Manchurian candidate", secretly "programmed" to kill Diana.
Other theories concentrate on a second car that was seen speeding away from the scene of the accident by several highly credible witnesses, including Gary Hunter, a British solicitor. Hunter said: "My own feeling is that [in the second car] these were people in a hurry not to be there. I am confident that the car was getting off the scene . . . It looked quite sinister." Hunter has never tried to profit from this story. ITV ran a documentary about the theories speculating that a strobe light could have been used to disorientate Henri Paul, or that the second car - which was never found, despite an exhaustive search - rammed Diana's limo into the wall of the Pont de l'Alma tunnel.
The conspiracy theorists are also divided over the motives for the "assassination". Mohammed Al Fayed believes that Diana was murdered on the orders of Prince Philip because she was expecting his son Dodi's baby. The Windsors, he says, could not bear the thought of a Muslim half-brother for Prince William. Several websites claim that Diana's anti-landmines campaign was threatening the international arms industry, so the weapons manufacturers decided to pick her off.
Who says? A majority of people in the Arab world believe that Diana and Dodi were murdered, and an Egyptian mini-series has depicted the Queen plotting the princess's death because she was meddling with Muslims.
How likely is it? We have yet to see all the relevant evidence. Richard Tomlinson, the former MI6 agent, said in a signed affidavit: "I firmly believe that there exist documents held by the British Secret Intelligence Service [MI6] that would yield important new evidence into the cause and circumstances leading to the deaths . . . in August 1997."
However, the motives offered so far seem pretty lame. Fayed has a history of bizarre statements, and you don't have to be a fan of the reactionary Prince Philip to find the idea of him murdering his own daughter-in-law (and MI6 actually carrying out his orders) absurd.
The other possible explanations, concerning Diana's humanitarian battle against the arms industry, are a tad more plausible. But absolutely no persuasive evidence has yet been produced.
5. The Muslims/the Jews (delete according to prejudice) were warned to stay away from the World Trade Center on 9/11
What's the theory? There are two mirror-image theories. One is that many American Muslims knew of the attack in advance. A Muslim student at a Brooklyn high school said to his teacher on 6 September 2001: "See those two buildings? They won't be standing there next week."
On 10 September 2001, a sixth-grade student of Middle Eastern origin at a Jersey City school warned his teacher to stay away from Lower Manhattan because "something bad was going to happen". Teachers at schools within sight of the World Trade Center in New York reported that, as the towers burned, many Muslim students were taking pictures: it seemed odd that so many of them happened to have brought their cameras to school on that particular day.
The other theory levels the same accusations at Jews. In the days following the attacks, several newspapers in countries of the Middle East reported that 4,000 Jews who worked in the World Trade Center had not gone in to work on 11 September, and that there were no Jewish victims. This was because Mossad (the Israeli secret service) had planned the attack in order to whip up hysteria against the Arab world.
Who says? The anti-Muslim theory has circulated in far-right circles in the US, but it has only been reported in Britain by the Telegraph columnist Mark Steyn. The anti-Semitic theory has had far wider circulation. A Gallup poll, taken a few months after the tragedy, found that most people in the Arab world believed the accusations were true.
How likely is it? Almost no evidence has been offered in support of either claim. Steyn cites only the "evidence" of a disgraced and sacked journalist on a suburban New York paper, and even that is for just one of several "facts" that he cites. Steyn did not even bother to try to back up his claim that Muslim students were taking photographs of the attacked buildings. I selected seven schools in New York City at random and called them; they all agreed that the idea was, in the words of one secretary, "horse shit". It is just about possible that one youngster, related to one of the attackers, overheard plans for 9/11 - but hundreds? Steyn seems to believe seriously that many American Muslims knew about the plan and did not warn anybody - not even the 300-plus Muslims who were murdered in the attack. This would fit Steyn's prejudice that all Muslims are cruel.
Similarly, the "4,000 Jews" figure used in sections of the Arab press and on European far-right websites is concocted. Nearly 500 Jews died that day. It is impossible to imagine Mossad directly attacking Israel's closest ally and most generous donor.