So let's start with arguably the grand-daddy of UFO conspiracy events, the supposed Roswell UFO incident. In 1947, the Roswell Air Force Base issued a press release saying that they'd found a mysterious metallic disc on a nearby ranch. The press was, of course, intrigued, but the base quickly changed their wording slightly: they'd found what appeared to be the remnants of a weather balloon.

The change was not quick enough. Of course, the local papers ran giant headlines saying that the air force had recovered a crashed alien spaceship. And in the years since, that story has stuck, as accounts surfaced from employees at the base that include multiple crash sites, massive cover-ups, and even a reported alien autopsy witch a film released in 1995 reported to depict the actual autopsy, but  its creator admitted that "most" of the footage was fake, thereby sort of discrediting all of the footage.

 ~Information found on io9.com