There's a conspiracy theory about everything - the Titanic never sank, Neil Armstrong never landed on the moon, Elvis Presley faked his own death, Michael Jackson isn't dead, Shakespeare was someone else - and someone put it aptly: "There is no conspiracy. It's good journalism."
JFK (released 1991) sheds light on one of United States' most enduring mysteries, the assassination of President John F Kennedy in 1963. Three years later, District Attorney Jim Garrison - played by Kevin Costner - finds too many coincidences, inaccuracies and conflicts in the investigation report (26 volumes) by Warren Commission. Interrogating several witnesses to the assassination, he and his team establish, beyond doubt, that Lee Harvey Oswald couldn't possibly have carried out the task single-handedly. Further investigation reveals that although all documents report three shots were fired, witnesses had heard up to six shots...
In the 1969 trial of Clay Shaw (one of the accused), Garrison provides more evidence that there were six shots fired and not as reported and that the single bullet could not have assassinated JFK and another person in the car. His theory is based on the fact that CIA got the president murdered and covered it up. Though Garrison lost the case, the end credits state that in 1979, someone (I have forgotten the name) testified under oath that Clay Shaw had been, once, a part-time agent of the CIA.
Whether you believe in the theory or not, it is an amazing movie. One of those movies, which - despite knowing the outcome - you end up biting the best part of your nails. A must watch (189 minutes)