People's psychology works in a strange way: For some reason, we like to assume that the world is not what it seems, but has some hidden reality, which is covered through conspiracies. Sometimes this is even true.

In the case of the lunar landings however, the matter is easily solved. They left many artifacts on the moon, which would be sort of difficult if they weren't there. They left a laser reflector for measuring from earth the rate of the moon orbit increase. This reflector is still in use today and can be detected with a relatively weak laser ray from any place and lab on earth.

http://en.wikipedia.org/wiki/Lunar_Laser_Ranging_Experiment

The problem with conspiracies is: If they are real and more than 3 people are involved, they always go public. You can safely assume that no real conspiracy would be likely to survive more than 10 or 15 years.