Looking back through the last 40 years, the Apollo Lunar landings really were the last achievement that can be defined as inspiring. While their astronomical costs in almost no way justified their scientific merits, that wasn't the point, the point was to beat the Soviet Union. And that's what happened because up until the United States made it to the moon, the Russians had the advantage in space.
Most everyone knows the moon landing story, but within the last ten years, theories concerning the landings, most notably that they were staged, have arisen. At first some of these ideas look as if they could be genuine, but to do some research it becomes very apparent that there base evidence is flimsy with no credible sources to be found.
Currently only about 11 percent of citizens in the United States believe that the government either staged the entire program, or at least part of it. And although this percentage is small, it represents an extraordinary amount of stubbornness on both the theorists part as well as the believers.
In order for the lunar landings to have been a massive conspiracy, it would have taken the cooperation, and continued cooperation of the nearly 400,000 NASA employees who worked on the Apollo program in addition to numerous foreign governments including the former Soviet Union. In 1970 a Soviet robotic probe called Luna 16 landed on the moon, collected lunar soil and returned it to Earth, this mission was followed by Luna 20 and 24 which did the same. Later the Soviet samples were compared to the American ones from Apollo, and they were all found to be composed of the same material. This comparison either represents a vast global conspiracy or more likely that man walked on the moon. And because the Russian probes were able to return only small samples as compared to the Apollo ones, they contained no large rocks or otherwise and so it would appear that humans must have gathered the Apollo samples as they were filled with rocks of all sizes.
Other avenues taken to disprove the lunar landings include saying the technology to do so didn't exist and in fact it did not, NASA had to invent almost everything that made it possible. NASA had possible. NASA had to invent various additions to it's space flight systems to withstand the increased radiation outside Earth's orbit. But even looking past the NASA's technological hurtles, the Soviets once again had comparable equipment that they used to fly plants and animals around the moon and back to Earth alive (Zond program). So it would seem that not only did the technology exist in the Unite States, but also in the Soviet Union.
However, most of the evidence that various theories present is based on photographs from the moon that have been obviously doctored, (air brushed, cut and pasting, etc) but this in no way proves the landing's themselves to be fake, as anyone who works in publishing will know that. Almost any published photo has been doctored in some way. It seems that if NASA were to spend billions of dollars on a fake landing that they would pay closer attention to the photos.
Although other so called "evidence" has been presented to disprove the landings, everything listed above should be enough to reason with.
Part of what science teaches is that one should not take everything as it is presented, but challenge it, and decide on the evidence. This idea in a modern sense stretches back to renaissance as well age of enlightenment. And one important thing that the inventors of the lunar conspiracies and many other conspiracies in general forget is that a rational conclusion needs to be reached, not one that forces the original idea that was to be challenged to be wrong.