I found this interesting quote on Wikipedia:
According to a 1999 Gallup poll, about 6 percent of the population of the U.S. has doubts that the Apollo astronauts walked on the moon.
"Although, if taken literally, 6 percent translates into millions of individuals," Gallup said of this, "it is not unusual to find about that many people in the typical poll agreeing with almost any question that is asked of them -- so the best interpretation is that this particular conspiracy theory is not widespread."
Nearly all interested scientists, technicians, and space enthusiasts have rejected the claim, considering it to be baseless.
One of the real problems with attempting to prove that the moon landings were real is that one wonders exactly what proof would suffice. For example, if we took close-up images of the moon and showed the landing sites and rovers, would this be convincing? Or would a hoax-proponent simply say that these photos were themselves part of the hoax? Thus, part of the problem with conspiracy theories is that they can easily become non-falsifiable stories, which means it doesn't matter what proof is shown, the believer will continue in belief.
In actual fact, the Japanese SELENE mission (http://solarsystem.nasa.gov/missions/profile.cfm?MCode=SELENE) will map the surface of the moon in high enough resolution that we should be able to see the landing sites and rovers that were left there. Personally, I'm pretty excited to see the images. But I'm confident that the conspiracy will live on. In fact, even when it becomes possible to go to the moon personally and see the original landers and rovers in a moon-based museum, there will probably still be people who say that we didn't land there in 1969.
As a quick note to the poster who questioned NASA's competence, I just want to note that the rocket technology for getting to the moon was in many ways simpler and better than the space shuttle. The shuttle was designed to be something that it could not reliably be, at least not with current technology. But the Apollo rockets were simple - giant, but simple - rockets with the payload on top. Also, as in all long-distance missions, course corrections were made on the way to the moon using current telemetry data, so it wasn't a matter of getting everything right on the first burn.
Getting to the moon was a challenge, for sure, but it was certainly within the technical capabilities of a group of intelligent people with government-sized resources.
Also, I just have to say that NASA has been doing a bang-up job on a lot of missions. Notably, the recent Mars missions have been stunning successes. The Mars Reconnaisance Orbiter, currently on its way to the red planet, will provide surface imagery with resolution better than you see on Google maps right now. There are some seriously talented people at NASA, and even though the failures make the headline news, they have been quietly pressing on with some amazing stuff.
SNG