Dozens of witnesses all describing the same craft, the government first denies it had reports, then admits it did. The FAA goes against its protocol and refuses to investigate the matter even though they will investigate a suspicious coffee container a day earlier. The hundreds of airport cameras in the area were magically "not working" so they were unable to show there was no UFO. This was, in my opinion, the most compelling UFO case I've come across. Oh, there was one civilian photo taken, and it was shown to not be doctored.
There are many great cases, but one of the best since it involved a US military nuke base in england was the Bentwaters event where the deputy base commander took a crew out and experienced it himself. One of the craft shined a light down in from of him, as he recorded it on his tape recorder.. The event happened over a couple of nights around xmas. One of the military police there was exposed to something which later gave him health problems, and he finally got the military to admit it, once they said they lost his medical records.
I dont know how much I believe in these UFO incidents, but to assume we are the only civilization in all of the universe is equally unbelievable. And I think it would be my easiest call as President to cover up any of these incidents unless they were 100% undeniable. The panic it would cause would lead to chaos.