I find many of the conspiracy theorists out there cling to implausible theories because, paradoxically, they're comforting:
Humans are thinking animals. Aside from high endurance for long distance walking, humans don't stand out very much, physically. Humans survive by their wits, detecting patterns and warning signs less intelligent animals would miss. Having special knowledge is an advantage, so it's natural to feel more secure when you know what's going on. Or if you think you know what's going on. Wisdom makes a person valuable and revered. That's why nearly every sort of woo, altie, or fundie pride themselves on being a "red pill": They have what they believe to be special knowledge. Of course, I find them to generally fail to prove it, but that's for the factual threads to cover.
On the flip side of the special knowledge angle is the fear of uncertainty. Many people, for example, couldn't deal with the idea that a lone gunman could kill the president during lax security, hence the need to assure themselves JFK had an enormous conspiracy of enemies out to get him. Many 9/11 twoofers can't deal with the idea that America could be successfully attacked in such a catastrophic manner, so they make up a special exception of an inside job of American conspirators.
To put it in geek terms, I found the Joker from The Dark Knight scary because someone like him could exist in real life:
I just did what I do best. I took your little plan and I turned it on itself. Look what I did to this city with a few drums of gas and a couple of bullets. Hmmm? You know... You know what I've noticed? Nobody panics when things go "according to plan." Even if the plan is horrifying! If, tomorrow, I tell the press that, like, a gang banger will get shot, or a truckload of soldiers will be blown up, nobody panics, because it's all "part of the plan." But when I say that one little old mayor will die, well then everyone loses their minds!There's no shortage of insane, violent people out there. Religious fundamentalism does a good job of encouraging those qualities. All it takes for them to cause chaos and panic in our lives is for us to get lax in security and/or them to get clever. If you're an overzealous conspiracy theorist, those sorts of people aren't a problem because it's all "according to plan" of some guy who manages to grab some sort of advantage in the end result. Without good evidence for a plan, about all you can say about those who benefit is that they're opportunistic bastards.
Additionally, there's so much in this world that's a result of stupidity. Popular idiots can get elected into office. People can fall for basic logical fallacies and in turn mislead voters with propaganda that results from those fallacies. People who should be experts in their fields can get sloppy or complacent enough to miss fundamental problems. This world is very much subject to Hanlon's Razor: Incompetence runs the planet far more than malice. Incompetence is harder to predict than malice, so it's more uncomfortable to deal with.