My wife recently got into Stargate: SG-1, a high quality science fiction television series that I was already a fan of.
The premise is that the United States Air Force is in possession of a "Stargate", a device that connect to other Stargates throughout the universe, analogously to a phone system, and send things there, including people. There are a wide variety of aliens in the universe at various technology levels from "just discovered fire" to "godlike", many of which did visit Earth in the past. The storyline proceeds from there.
It reminds me of why I don't believe in a real governmental conspiracy for aliens. In the show, the Stargate is top secret... but literally thousands of people know about it, from high in the military, to research scientists working on the various technologies brought back and their support staff, to various civilian spy agencies, and even including members of (at least) the Russian and Chinese governments and significant portions of the legislative bodies of at least the US and Russia. Unlike the Manhatten project, these people are scattered throughout the world in a wide variety of positions and with a wide variety of philosophical and political affiliations.
It is virtually inconcievable that such a thing could be kept secret. For instance, in the show there are by my count at least 10 episodes that would be dead giveaways; unexplained explosions and quaratines, time distortions well within the detection range of civilian equipment, unexplained and clearly unnatural celestial phenomena. And all the people who would have to know to obtain any benefit all keep quiet?
Governments are OK at keeping small secrets but given their competence in other areas, it is virtually inconceivable they could keep a large one like this, covering thousands of people over tens of years. They would all be, after all, only human.
Thus, I do not believe in any "Alien Conspiracy" theories; if there are aliens floating around, they are doing their own dirty work, not going through human intermediaries.
Also, I highly recommend Stargate SG-1, if you are into science fiction television at all. It makes Star Trek look like a hack job, and I speak as one who used to really like Star Trek. (Increasingly, I'm coming to see the whole thing as kind of fun, but not somewhere I'd want to live... for instance, the Federation is Communist in Star Trek: The Next Generation. Fun stories but I'd rather live here.)