Moon landings were real - way too many non-NASA people all over the world were monitoring the radio transmissions, tracking on radar, etc. At the very least, it would have been noticed if the radio transmissions were from somewhere in the Nevada desert. (I don't understand FabbyChic's assertions - maybe there's a confusion about the moon's gravititational attraction in that 1/6th has been read as 6x?)
Diana - just an accident. As others have said, there's no plausible way her death could have been planned as there were too many variables. People have survived horrendous car crashes, so there's no way that even a planned car crash at a particular place and at a particular speed could have a guaranteed result. I do find this particular conspiracy theory disgusting, for much the same reason as razzlebathbone has said.
As for the 9/11 conspiracy theory: It was "a small faction" of the government. And the reason? "The Cold War's over. But with no clear enemy to stockpile against, the arms market's flat. But bring down a fully loaded 727 into the middle of New York City and you'll find a dozen tinpot dictators all over the world just clamoring to take responsibility, and begging to be smart-bombed."
All of what I've quoted I've copied from a transcript of the first episode of a TV show that aired in the US in the March of 2001. And that fictional story did involve a passenger plane being flown into the World Trade Center. That TV show was called The Lone Gunmen and was made by the same people who made the X-Files - probably the most influential TV show in recent times in terms of conspiracy theories.
I think there are too many people who can't distinguish fiction from fact - probably because fact doesn't have the same wow factor. And the conspiracy theories about the WTC attacks are as disgusting as the Diana conspiracy theories.