Stories of the military covering up UFO sightings have been popular since the 1950's and continue to be reported to this day. Given the volume and frequency of such reports, the question is what rather than if people are seeing things in the sky, and why or if the military has some kind of vested interest in suppressing these sightings.
Of course the explanation that many people ascribe to is that there have indeed been alien visitors to our planet and that the military have hidden this information from the public, worldwide, since at least the 1950's. It seems a strange coincidence however that these mass sightings began in earnest after the second world war, when countries such as America, Britain, Russia and the like began to experiment with new types of aircraft.
Not to mention the fact that even for the military, keeping that kind of information under wraps would necessitate thousands of people colluding in the cover up, without any of them ever going public with conclusive proof. This of course hasn't happened, suggesting that any cover ups that the military have staged at the very least haven't involved aliens.
Much smaller scale military and governmental incidents and crimes are brought to light all the time, and rarely remain covered up for any great length of time before someone usually unwittingly, exposes the truth. As powerful and organized as the military and government are, they are still fallible, and rely on the imperfect decisions of humans. The idea of this convoluted mess of a system being able to keep something as massive as aliens under wraps then becomes extremely unlikely.
Although it may appear that the military attempts to cover up UFO sightings however, a perhaps more likely theory at least in modern times is that in many cases they actively encourage these sightings as a means if distracting attention from their real activities.
Its no secret either that the military regularly tests experimental air craft, or that the majority of supposed UFO sightings tend to take place very close to military facilities. By doing an intentionally half-hearted job of covering these 'sightings' up, less attention is paid to the fact that these aircraft are being tested, and more attention is instead given to theories such as aliens being behind the UFO's and the like.
By allowing every crack pot and half wit who thinks that they have seen something in the sky, simply wants some attention or in some cases may be unknowingly suffering with a condition such as sleep paralysis to get attention, the very small proportion who might have seen something out of the ordinary are marginalized and lose much of their credibility. Not to mention that they don't get nearly as much attention due to the fact that there are so many reported sightings every year. Far from covering up UFO sightings then, the military could well be encouraging them, regardless of whether they have anything to hide themselves of not.
Certainly with the kind of power that they wield, the military could do a much better job of keeping the throngs of tourists and conspiracy nuts far enough away from bases such as Area 51 that they couldn't see anything worth taking grainy unfocused photos of. By perpetuating the myth that they have something to hide, what they are doing in plain sight, testing experiential aircraft, is overlooked.
Not to mention that in many of the famous UFO hot spots, the local economy is now so entrenched in the folklore of sightings and encounters that they depend almost entirely on the tourist trade. To stop the supposed cover up of these incidents would cripple such places, and as such allowing stories of cover ups to perpetuate in many cases helps to keep these towns prosperous.
Similarly to UFO sightings, the military has also accused in the past of covering up reports of crop circles and other at the time strange phenomena, until they were unequivocally debunked. In the case of crop circles, (which some people still believe are not man made) admission from various groups around the world that they are in fact created by using a plank of wood, rope and surveyors tape, and not aliens.