I admit it, I'm highly skeptical of conspiracies like the 9/11 Truthers, Flat Earthers, etc...
The way I see it? "these things always come out in the end, see for example the Gulf of Tonkin incident, or Hitler's various false flag operations that fooled no one. So conspiracies don't work and a worldview based on their generalized, or at least frequent, existence is problematic."
Edit: Please note that this is asking about cases that successfully deceived the public for more than 25 years. A number of suggestions were made that would qualify, except that the mess blew up before 25 years were up. So, by definition, nothing that happened before 1994 is in scope as of 2019. And even if it predated 1994, there is the criteria that exposure took at least 25 years.
There is a big flaw in my reasoning. If you discount conspiracy theories just based on the ones you know of that did not work, that doesn't account for the ones that did because no one found out. And if they worked because no one knew of them so they can't be used to prove that conspiracies do exist and do affect our governments.
So, what are some known examples of conspiracies that worked from the point of view of the perpetrators?
Needs to involve a nation state, possibly in collusion with a commercial entity. Not just a commercial entity: one knows not to expect honesty from tobacco companies for example.
It needs to have affected national policy and a large number of people, preferably negatively, in that state. I.e. shady deals to secure oil fields in a far away land isn't necessarily something that voters have historically cared much about.
However, starting a war between your country and a foreign state under false pretenses certainly counts.
The people being fooled, citizens of that state, would need to have felt strongly negative if they had found out. i.e. no "harmless little white lies at election time". Again, that brings in a notion of active harm to the citizens at large.
The conspiracy needs to be secret, have fooled, or at least been disbelieved, by the general public. Going back to tobacco companies, no one really believed their lies. And that also rules out the Gulf of Tonkin as it has always been strongly disputed. Global warming is also out as whatever side a government takes, either "wrongly disbelieving it" or "acting too strongly on unwarranted assumptions", the public is already well aware this a major policy issue.
The state in question needs to be, or at least pretend to be, a democracy with a free press. It's all to easy to come up with cover ups in totalitarian states. And if there's no press, it's not obvious how people would hear of the misdeeds.
How do we judge success?:
The perpetrators need to have benefited from it. But since we need to know about it, I'll arbitrarily say that, if the facts only came out after a generation (25 years), then the con was successful as the people doing it have likely retired and/or statute of limitations have kicked in.
Note that this 25 year limit also aims this question at historical events, rather than current events where the facts are still up for debate.
And, it needs to be now generally accepted by historians that it was actually a cover up/conspiracy.
Feel free to edit and/or ask clarifications. I tried to frame it to include only the typologies found in some of the big common conspiracy theories involving governments found nowadays like inside job 9/11, Flat Earth, faked moon landings, vaccine scares, etc... I specifically want to rule out things like say a car company for example successfully covering up exploding gas tanks on its own - a government needs to be in the lead. Ditto government positions that were not in the best interests of its citizens but were already widely known at the time - secrecy is key in a conspiracy. While certainly negative, things like the Hanford nuclear plant's release of radioactive material isn't really what I have in mind as it's not an attempt to affect national policy.