In 1999 one of the best (and perhaps strangest) science fiction films premiered in theaters. That film of course is The Matrix.
The film itself was visually stunning, it's fight screens were so awesome that other films have duplicated the same style in their fight scenes, and it had that was really unique story line... and made anyone who watched the film not sleep for a few days.
The film itself also had multiple concepts in it that many conspiracy theorists tend to use in their beliefs.
In fact many concepts from the film have either inspired conspiracy theorists in their and terminology and their beliefs, or were inspired by conspiracy theories and conspiracy theorists, such as:
The world as we know it is a lie.
The first concept in "The Matrix" that many conspiracy theorists hold near and dear to them is that the world as we know it is just one giant lie, and that everything we know is fake and intentionally constructed in order to fool the masses.
In the movie Neo is told that the world is a lie, and is eventually shown that the whole world that he knew is a computer generated simulation. While most conspiracy theorist don't go as far to say that our world is a computer generated simulation (although some do) many do think that everything we know is just one well constructed lie, and that all of our history has been guided and constructed by some force that we don't know about.
Only people who "wake up" can know the "truth".
In the movie Neo is told that in order to know the truth about the world that he would basically have to "wake up", which is something that conspiracy theorists tell people all the time that they need to do (especially when they express doubt in the conspiracy theorist's claims).
Whether the concept of "waking up" came from the movie or not, anytime one argues with a conspiracy theorist (especially on the internet) often the conspiracy theorist will tell the person to WAKE UP to the "truth" (whatever that may be for the conspiracy theorist).
People must choose if they are to "wake up" or not.
Half way through the movie Neo is given a choice about whether he wants to find out what the Matrix is in the infamous "blue pill, red pill" screen. In the screen Neo is given the choice of taking a blue pill and continuing life as he knows it, or taking the red pill and finding out the truth about the world.
This screen is so infamous that many conspiracy theorists now commonly reference to the blue pill and red pill when trying to convince someone that the conspiracy theory that they are promoting is real, and that the only way that the average person can learn about what is really going on in the world (at least from the conspiracy theorist perspective) is that they must "choose" to "take the red pill", or that they must choose to "wake up".
The world is controlled by a shadowy group.
One of the biggest beliefs that conspiracy theorists have is that the world is controlled by a shadowy group, and that only those that have "woken up" will realize exists.
Now in the movie of course this is the machines (although this is just a name that the humans give them, as there is no actual name for the machines) but in reality the closet thing to the machines would be the "Illuminati", another shadowy group that controls the world (according to conspiracy theorists), and that only those that have "woken-up" even realize that it exists, while for the rest of us we don't believe that it exists because there is no evidence that it exists(or at least none that us "un-wakened" people can see).
The shadowy group is exploiting humanity for it's own purposes, and the people don't even it.
In the movie Neo is soon told not only what the Matrix is, he is told just what it is for (that is of course to keep humans ignorant of reality while the machines harvest their bio-electrical energy).
While most conspiracy theorists won't go as far as to say that, most will say that an alleged shadowy group (again, usually the Illuminati) is manipulating humanity, and exploiting it for it's own purposes (whatever that may be) and that all events that happen in the world are being created and/or manipulated by this shadowy group for whatever it's reasons are, and that we are all just pawns for this group to be used in whatever way they feel like.
The shadowy group sends out agents to destroy those that oppose it.
The primary villains in the movie (besides the machines) were the Agents, a group of computer AI simulations that were sent out to kill anyone in the Matrix that had been awakened and were now opposing the machines. Ironically (or not) these agents look like members of the Men in Black.
Many conspiracy theorists also believe this as well in a way, in that the shadowy group which they are opposed to is sending out agents in order to destroy them, usually by way of discrediting them, although many conspiracy theorists do seriously believe that these so called agents will kill them if they can, and that they have killed people before in order to silence them.
Anyone who has not "woken up" can be turned into an agent.
In the movie Morpheus explains that anyone who has not been "woken up" or removed from the Matrix can unwillingly become an agent, and thus anyone whom has not woken up is a potential enemy.
This belief is also common with many conspiracy theorists as well, in that they believe that anyone whom has not woken up (I.E. those who do not believe in the conspiracy theories that they believe in) could either be an agent (commonly called a shill) or a potential agent (commonly called a sheeple) and might even become one without their knowledge (commonly called a sleeper agent).
Only those that have "woken up" can fight this shadowy group.
In the movie it is made quite clear that the only people who can oppose the machines and their AI programs within the Matrix, and fight them and save humanity, are those who have "woken up".
Many conspiracy theorists basically believe the same thing (minus the machines and the computer generated reality) and that they are the only ones that can fight these so called "shadowy groups", and they believe this because they have "woken up", and thus, according to them, are aware of these so called groups. This is also why they try to "wake up" so many others, so that they can also help in their "fight" as well.