According to documents listed on Wikipedia, "Operation Northwoods" would have given the US 'reason' to go to war with Cuba...

The plot, presented by the Joint Chiefs of Staff, included a scenario in which a US aircraft would 'fake' being shot down by Cuban aircraft, then flee the area at a low altitude to a 'safe' base.  Once at that base, the aircraft would be re-designated (tail number changed), the pilot would be returned to his regular duty (he would have assumed a fake name for the mission), and submarines would 'release' aircraft parts near the area of the purported attack.

Why didn't any of these events take place?  President Kennedy would not approve.  And, in 2001, when Cuba officials found out about the proposed plots, they were none too happy about them.

With documents like this one making it's way around the interweb, I can see why there are so many 'conspiracy theorists' out there!

 

(Via Cuba.cu, Wiki)