A large group of people - collectively called the 9/11 Truth Movement - cite evidence that an airliner did not hit the Pentagon and that the World Trade Centre could not have been brought down by airliner impacts and burning aviation fuel alone.
This final group points to video evidence which they claim shows puffs of smoke - so-called demoliton squibs - emerging from the Twin Towers at levels far below the aircraft impact zones and prior to the collapses.
Something did crash at Roswell, New Mexico, sometime before July 7, 1947 and - at first - the US authorities stated explicitly that this was a flying saucer or disk - as shown by the splash story on that day's Roswell Daily Record, pictured.
As with the assassination of JFK, the official inquiry into the events - the 9/11 Commission Report - is widely derided by the conspiracy community and held up as further evidence that 9/11 was an "inside job".
Scientific journals have consistently rejected these hypotheses.
A report by the Office of the Secretary of the Air Force released in 1995, concluded that the reported recovered material in 1947 was likely debris from a secret government program called Project Mogul, which involved high altitude balloons meant to detect sound waves generated by Soviet atom bomb tests and ballistic missiles.
A second report, released in 1997, concluded that reports of alien bodies were likely a combination of innocently transformed memories of military accidents involving injured or killed personnel, and the recovery of anthropomorphic dummies in military programs like Project High Dive conducted in the 1950s.
At the milder end of the spectrum are the theorists who believe that the US government had prior warning of the attacks but did not do enough to stop them.
Others believe that the Bush administration deliberately turned a blind eye to those warnings because it wanted a pretext to launch wars in the Middle East to usher in another century of American hegemony.
The ten-month investigation of the Warren Commission of 1963 to 1964, the United States House Select Committee on Assassinations (HSCA) of 1976 to 1979, and other government investigations concluded that the President had been assassinated by Lee Harvey Oswald - who was himself shot dead by Jack Ruby while in police custody.
But doubts about the official explanation and the conclusion that Oswald was the lone gunman firing from the Texas Book Depository overlooking Dealey Plaza where Kennedy was hit surfaced soon after the commission report.
In 1979, the House Select Committee on Assassinations (HSCA) found both the original FBI investigation and the Warren Commission Report to be seriously flawed.