Gorrammit! The Government already released the Roswell documents (like 3 years ago now i think) that provided a perfectly reasonable explanation for the whole incident:
(yay narrative form summary!)
Roswell airbase, nice, secluded, the perfect place to test new spy equipment without anybody, much less the Russians, finding out.
One day they test a new type of spy balloon that is undetectable by radar and needs no propulsion as it takes photos flying over enemy territory.
Unfortunately, during the test the spy module detaches from it's balloon and lands (crashes) in a nearby farmer's field. Air force personnel from the Roswell base scramble to gather up the device before the anyone else does (which would blow their cover seeing how they're testing some top secret shit here). But, the farmer gets it first and the papers catch wind of it and prepare to publish this amazing find in tomorrow's newspaper.
The army at this point is shitting themselves as due to their cock-up they think tomorrow's headline will be something like: "Farmer discovers America's top secret spy operation!" or "Russia furious at USA's work on spy equipment!" and therefore the whole secret spy on the communist war machine plan goes down the drain.
Then the next day the headline is "Farmer finds Alien UFO!". And the army breathes a sigh of relief. Deciding to run with the story to quell any suspicion from the Russians, the government makes several "leaks" (including that they captured an alien) and remains as tight-lipped as possible to make it look like they're hiding something about the incident. Even the president visits "in secret" to make the whole thing look serious.
So the army and the government successfully dodge a very serious diplomatic bullet during the cold war and are able to use these spy devices while the news and public are left chasing their own tales about aliens and UFO's.
One must not forget that the intelligence arm of the government is VERY good at keeping secrets if they want to and most popular conspiracy theories are sometimes perpetuated by government intelligence agencies to keep the public in the dark until the secret no longer matters.
So you can see how with a stroke of luck and a little quick thinking and deception the government was able to start up this conspiracy intentionally to avoid the public and consequently the cold war enemies finding out about spy operations because of a cock-up at the Roswell airbase.
The truth is out there: But conspiracy theorists have no fucking idea.
[side note: the famous photo of the 3 lights in the sky is supposedly the camera flashes from the spy probe that crashed]