When the classic SF film The Day the Earth Stood Still came out in 1951, Project Blue Book reported the largest number of UFO reports in its history (it officially ended in 1969), including a famous UFO "flap" over Washington, D.C. - funny enough, the very place the alien spaceship landed.

http://classics.www5.50megs.com/gort/index.htm

Other UFO flaps also happened after major space exploration milestones and even natural disasters.

I wish I had the exact reference, but I do recall an item in an issue of Omni Magazine from the early 1980s where someone reported a fake UFO story on a radio talk show. Within hours, not only had they received hundreds of phone calls from people claiming to have seen the UFO as well, some even went so far as to say they had been abducted by the alien ship's crew!