I've wondered about this one for a long time.
A: You're a bunch of sheeple who believe whatever you're told!
B: Then why don't we believe you?
From what I've seen, it looks psychological.
Leaving the grifters to the side, it has the feel and appearance of people needing there to be an explanation, a reason for why bad things happen. The idea that bad things happen, for no apparent reason, just doesn't sit with them and leaves them feeling powerless, and so they need to have a cause, a THEM that are behind all the bad things that happen in the world, so that the average HB can sit there and say "see, it's not that I have no power or control over my life, it's because there are big, evil, force controlling the world for there own nefarious (moustache twirling) ends", or something like that.
And, of course, once you have a big bad THEM in position, you can start tying them into everything bad that happens; plane crashed? Must have been a person on board that THEY wanted to be rid of. Fires burn down a town? Clearly THEY were testing their new DEWs. Local football team lost? Well, look at the position of the moon, and the uniform number of the full-back, clearly it was a ritual "sacrifice" (that they have to perform in the open, and give clues that they are EVIL - because reasons).
Now I like a good conspiracy, but it needs to make internal sense. The average moon landing hoax doesn't make sense, when you look at it from a story point of view. There was a good one, Richard Hoagland's solar system wide conspiracy that you used to find on Enterprise Mission, that I liked. It told a good story, that didn't fall apart with just a casual brush. Of course, once you started poking at the details it stopped making sense, but the overall story was fun.
