The basic setup here is as follows: Turn a politician's son-in-law into a war hero by murdering some and brainwashing the others of his platoon stationed in Korea (brainwash him, too). Then use his notoriety upon returning to rocket him to the White House as a vice-presidential candidate, then use your brainwashed candidate to assassinate the presidential candidate. This is the plan that the communist (and supposed anti-communists) use in "The Manchurian Candidate, an incredibly suspenseful political thriller that's as resonant today as it was when it came out in 1962.
One of the best conspiracy thrillers of all time is unfortunately based on a real case-that of Greek politician Grigoris Lambrakis. The director makes his intentions clear in the opening credits with this message: "Any resemblance to real events, to persons living or dead, is not accidental. It is INTENTIONAL." The movie is as bold and uncompromising as that opening shot across the bow would indicate.
How are conspiracies born? That's the question being addressed in "Executive Action," a movie about the plot to kill JFK. In it, various businessmen and politicians hold a secret meeting to discuss how, why, when, and where the dirty deed will be done. None of it's based on anything that's been proven, of course, but perhaps that just means the conspiracy to cover up the murder was especially effective, right?
For another, larger-scope look at the same conspiracy, check out Oliver Stone's "JFK." That movie is about New Orleans District Attorney Jim Garrison and his fight to try and convict a local businessman/possible CIA agent for the murder of John F. Kennedy. Like Garrison, Stone throws every possible theory of who, how, and why the assassination happened at audiences, with only one possible conclusion to be drawn: We will never know the truth.
Not all conspiracies are global: Frank Serpico, the real-life New York City cop played by Al Pacino in the movie, tried to bust one up that just took place within the NYC Police Department. The conspiracy was to keep their system of bribery and corruption alive, and Serpico got shot in the face for his troubles. But, he also got to be played by Al Pacino in a movie, so maybe it was worth it.
"The Parallax View"
Warren Beatty is a journalist who accidentally stumbles upon a conspiracy that's almost too wild to believe: A large corporation is seeking out possible assassins, to be trained and then sent out to eliminate high-power individuals perceived as a threat to the status-quo. This exciting thriller is carried out with such exacting control by director Alan J. Pakula that it might be easier for audiences to believe the truth of it than other supposedly "based-in-fact" conspiracy movies like "JFK."