The Moon Landing didn't occur though just for Americans to pat themselves on the back. It was a competition for prestige, like most of the Cold War, trying to get the gain influence over the rest of the world. It wouldn't matter so much what Americans thought if the Soviets produced proof that the US didn't go to the Moon, it would be what the whole world would think.
The late 1960's and early 1970's were not a glowing time for the States (Vietnam was prattling on, Nixon had begun is shenanigans, Civil Rights Movement, the deaths of Robert Kennedy and Martin Luther King Jr.). If the Soviets could have come down and said 'look, even your so called victory is just a sham, and so are you' they certainly would have, and something like that could have been devastating at the time.
But they didn't do anything like that, instead of delivering a monumental blow to American credability and prestige, they allowed it to be a victory that was watched the world over. So really, either they knew it was for real and couldn't risk the embarrassment of claiming otherwise or the monolithic KGB and very bright Soviet Space Program couldn't see the what some random independent investigators and a Fox television program did. There is interesting analysis of the photos and and film from the moon, as well as some interesting recreations floating around, nothing has really surprised me about it or pointed to it all being in Arizona.
For 9/11 things, I think it's very unlikely for the simple reason that the US Government leaks like a sieve. Really only select Black Budget military projects (which are carried out literally in the middle of the desert and probably a lot underground) can stay relatively in the dark, and most of what people think they know may be disinformation. When you talk about conspiracies of hundreds or thousands of people all over the country, things start getting less and less likely. Compound that with the amount of money and fame a single conspirator could make by coming forward with "the truth" and it gets very unlikely.
I don't doubt small numbers of people can participate in conspiracies (the Assassination of Lincoln, for example) but the more people who come into play, especially if they're government workers, the more chance that something will go wrong. There's a great quote out there, it goes something like 'More often that not, conspiracies fail, but even more often, they never existed in the first place.'