Apollo conspiracy theory
The "evidence" for this demonstrably false belief includes the allegation that the American flag placed on the Moon appears to wave in the windless lunar environment, the absence of stars in the lunar sky in photographs taken on the Moon (an effect of the speed of the film the astronauts used), and the allegation that shadows in the photographs run in different directions, rather than parallel, as if the sun were not the source of light. Additionally, some point out that when shaded by the landing module, the astronauts should appear shaded. Rather, they appear well lit.
These claims are easily refuted: the flag was made stiff by rods inserted into it, and thus small vibrations, say from an astronauts hand, were amplified. If the exposure of the camera had been set high enough to see stars, the lunar surface would have appeared blindingly white in photographs. And shadows can appear to fall in different directions on uneven ground. Additionally, the varied surface of the moon reflects light, making objects which should be shaded well lit.
NASA notes that it can be conclusively demonstrated scientifically that the astronauts really went to the moon. One of many possible demonstrations uses ground lasers reflecting off mirrors placed by astronauts during their visits.