The philosopher Plato once posed the Allegory of the Cave in his work, The Republic. He thought that, if prisoners spent all of their lives chained in a cave and facing a wall, their only experience would be watching the shadows on that wall. They never understand that there are things beyond that wall. The philosopher, however, is freed from that cave and can begin to understand the nature of actual reality. This may look like stoned sophomoric wonderings with some bragging tacked on at the end, but it laid the groundwork for a lot of science fiction premises. There are plenty of minor conspiracies and cover-ups in the world, but some go beyond minor plots and conceal the fabric of reality. Have a look at all the agencies, societies, guilds, and collections of friends that like people to be kept chained up in a cave.
The Adjustment Team from "The Adjustment Team"
Yes, the movie changed the 'team' in Philip K Dick's short story into a 'bureau', possibly because a 'bureau' sounds larger and more impersonal and possibly because they wanted to avoid a million 'A-team' jokes in the reviews. (It didn't work here, Hollywood. No mercy!) The A Team in the novel is more out-and-out supernatural, as well as being unambiguously good - they're working to keep the world from descending into nuclear war, and not concerned with Matt Damon's love life.
The Nibblonians from Futurama
These cute little three-eyed space raccoons had a hand in pretty much everything, from keeping tentacle monsters out of the universe to forcing people into time travel in order to defeat a secret race of giant space brains, to fueling the universe's starships. Thanks to well-placed smacks to the head and memory-wipers, they worked undercover and unknown for thousands of years.
The Legion of Madfellows from Futurama
Futurama is strong on conspiracies. In The Wild Green Yonder it turns out a group of guys in literal tinfoil hats have been keeping life from being extinguished by The Dark Ones, who are locked in a struggle with the benevolent Encyclopods. They keep their secrets with a bottle to the head of anyone who guesses what they're up to, but those that don't get a bottle-lobotomy will simply be killed by the Dark Ones, keeping this conspiracy under wraps.
The Watchmen from Watchmen
This conspiracy's tough to classify. Yes, there is a massive conspiracy meant to keep people from knowing something, but is the conspiracy evil or good? And who exactly is part of it, those that actively participate or those that just stay silent and make the best of it? And is the conspiracy meant to keep people from knowing the real ugly truth about the world or is is meant to make them let go of petty, arbitrary conflicts and really see reality? Oh, Alan Moore, you mischievous scamp. You keep us guessing.
Wanted is based on the idea that we really do live in an age of superheroes, supervillains, and wondrous superpowers. The only problem is, the supervillains beat all the heroes and brainwashed the world into thinking that the past real exploits of the heroes were just comic books. This doesn't seem to work out for anyone. Characters out-right say that the food tastes worse and the colors are darker. Even the happiest villains hit the wall when it comes to mayhem. And now, instead of just walking away from the scene of their crimes, they have to clean them up and dispatch a crew to wipe people's minds. Hardly seems worth it.
The Men in Black from The Men in Black Movies
Guys in black suits run around covering up alien activity. Sometimes they're Will Smith and they do it with style. Sometimes they're Tommy Lee Jones and they do it looking like a basset hound, but cooler. What matters most is there are aliens living among humans on earth, but anytime a human gets a glimpse of them they're treated to a neurolizer - a flashing light that wipes out the memory. The only odd thing about the Men in Black is that they actually wear suits and ties, like they're in Reservoir Dogs or The Blues Brothers. At this point they'd be far less likely to be noticed if they were the Men in Black T-Shirts.
The Men's Club in The Stepford Wives
This group only alters the reality in their little corner of the world, but they manage it quite well. Their plan to replace all their wives with submissive, permanently-cheerful, sexbots makes Stepford into an alternate reality - not based in the fifties, but in a fifties TV show.
The Vampires from the Blade series
Vampires rule the world from large corporations. They live forever. They have human slaves. Law enforcement officials will do anything, because they want immortality and power. Vampires are a greater reality in the Blade universe. What's strange is that, in the Blade universe, nobody tells on the vampires. It seems like the people fighting against them could produce evidence that they exist pretty quickly, and then they wouldn't be fighting alone.
The Aliens from They Live
These aliens gets points for completeness; they take over government and industry, and plaster the world with subliminal messages. They lose some for unnecessary frills. Their main goal was getting the earth to thicken its atmosphere. We were already on our way. All they would have needed to do was tell each person they reached through their elaborate conspiracy that they could look at a real live alien if they found a way to cut down ten trees and burn them and the whole thing would have been done in a couple of months with no lying.
The Precrime Squad in Minority Report
On the face of it, this just seems to be a conspiracy to abuse power - like many other minor conspiracy thrillers - and not a giant cover-up of all reality. However, since this abuse of police authority involves psychics, it tampers with the giant spiritual question of free will versus destiny. While there's no doubt that the Precrime Unit was part of a dystopia, I feel that the movie came the wrong conclusion about the legitimacy of precrime punishment. We already convicte people falsely. Might as well do it before anyone gets killed. And if the supposedly saved victim does bite the big one, there's proof-positive that they've got the wrong suspect. If anything, it's a better system than what we have. That seems like it's worth occasionally arresting Tom Cruise. Still, the Precrime Unit tampers with the great question of destiny versus free will, and so covering up mistakes makes for a big conspiracy to conceal reality.
The Government in the X-Files
These guys are so good that I don't even know what they were trying to do. The problem is, I don't think that they knew either. It kind of seemed like the entire government played a game of telephone and each agency went off to work on whatever they'd 'heard' the last agency whisper; so one genetically engineered bees, and another designed a computer chip that lodged in people's noses and cured/caused cancer, and another just stabbed people in the neck to see if they melted.
The Strangers from Dark City
If anyone is good at their job, these guys are. They change where we are, what we are, and who we are, and we never catch on. We don't even catch on that it's always night or that we're flying through space on an alien space ship. To put that in perspective - half the holoroom constructs in Star Trek figure out they're flying through space on an alien space ship. Either the Strangers are very smart or we are very dumb. It's only when a freak of evolution comes along, with the same abilities that the Strangers have, that things go south for them.
The Machines in The Matrix
Many of the rest of these conspirators lost out at the end, either due to incompetence or bad luck. The machines in the Matrix pretty much won. They made the people who had used them as slaves into their food source and they created a world so hostile and miserable that much of their food source would turn away from reality anyway. They created the perfect 'shadows on the wall' conspiracy - the one in which the shadows are better than the reality.