Firstly, the Cold War. At the height of the Cold War, winning the space race would have meant either the USA or the USSR getting ahead of the other. This means that if there were any way for the USSR to degrade or discredit the USA, they would have found it; furthermore, no conspiracy on that scale (NASA has around 18,000 employees) would have been kept secret, so it would have been incredibly easy for the USSR to find out if it had been fraud. Secondly, photographic evidence. It seems obvious, but the sheer number of photographs - none of which show anything terrestrial - is pretty compelling evidence. Lots has been said about light sources, errant shadows and all that, but this is all based on how light behaves on Earth. The moon has no atmosphere to speak of, and so refraction and reflection will be slightly different. The Lunar Module was covered in reflective paneling, and so would have had a major effect on the way light was reflected onto the surface. The texture of the moon’s surface would also have an effect on shading. The lack of stars has also been cited as evidence against the moon landing, but the cameras were set to daylight exposure and would not have picked up the stars, so that is also unsatisfactory proof. Thirdly, 382kg of rock from Apollo missions 11 and 17 which is universally acknowledged as being non-terrestrial. It is identical to the Soviet samples: as I've said before, if there were a difference the USSR would have pointed it out. It is interesting to observe that out of all the people who have claimed the moon landings were faked, not one of them had any direct involvement with the program. I think that's pretty conclusive.
Finally - I believe this is my most important point - the USA has gone to the moon SIX TIMES. It would have been the height of impracticality to fake a moon landing six times. Surely, if it were a conspiracy, they'd have left it at the first hurdle and not dug themselves a deeper hole? In my opinion, conspiracy theorists need to stop trying to diminish the moon landings: they were incredible feats of human intelligence.