In a nutshell operation paperclip was a mean's for the US military to smuggle various Nazi scientists and intelligence officers into the US who would most likely not be accepted due to their ties with the Nazi party and crimes they would be charged with otherwise. While it is almost a given that the information and help that was given to the US by these people helped give us an edge in the Cold War, it has been said that some of these Nazi's used their information to make things worse between the US and Russia (making the Cold War worse than it would have been otherwise) and by making US intelligence agencies further their own goals at the expense of the US taxpayers.
As far as I know this is one of the few conspiracies that the US government doesn't even bother to deny.
John F. Kennedy assassination
I'm sure almost everyone has heard of a conspiracy theory about JFK being assassinated by someone other than Oswald and/or that Oswald did not act alone so I won't rehash some of the basics about this one. The only things I remember about this one that are interesting is that at the time of it happening JFK was butting heads with the CIA and the military industrial complex as a whole, JFK's assassination supposedly closely followed some of the things outlined in a book written by the CIA about how to carry out an assassination in a banana republic if they ever needed to do so, and the vice president at the time of the assassination waited no time at all to take over the role as president and steamrolled the process before any one had any time to really process what had happen. Also it is kind of odd that Oswald was immediately assassinated himself (while in police custody) which made it impossible for anyone to ask Oswald much about it.
Project MK-Ultra is another one of the conspiracies in which the US government no longer bother to deny. It is basically one of the CIA programs in which they experimented with mind control in the hopes that they could discover something that might be useful against Russia/China and or in the Cold War. While the idea of the CIA conducting illegal and/or unethical medical experiments on prisoners it's on citizens in order to gain an edge on the Soviets, it kind of begs the question as to what other projects they have done in which they may have crossed the line.
Roswell (as well as UFO conspiracies in general) are kind of a large topic and somewhat hard to generalize. Why it is difficult to prove that nothing other than a weather balloon crashed down in Roswell, just as it is hard to prove that there is anything more to the JFK assassination than Oswald shooting him, there seems to be several inconsistencies to the government account as to what happened. For example if it was merely a weather balloon, then it is highly unlikely that the people reporting the "UFO" would have made the fantastic claims that they did if there was any chance that the object was man made and mistaking a weather balloon or any other similar object as a "UFO" would destroy any professional and personal integrity after they made such a false claim. The fact that the military didn't discharge or take other actions against the personal making such erroneous judgments makes one wonder if they claims were erroneous after all or if the government really just wanted to put the matter behind them. Also it is worth noting that Roswell is far from being an isolated incident since many WWII fighter pilots encountered 'Foo Fighters" (ie. UFOs that existed before the term UFO came about) and there are even cases of planes crashing and pilots getting killed during such encounters and the US military not bothering to investigate/follow up on such crashes since it is a given such events are always due to "pilot error" or mental condition at the time of the crash/disappearance. Also I believe that when the US government agency responsible for accounting and record keeping investigated Roswell base at the time of the incident they didn't find anything, but that was because every record from several months before and several months after the incident had already been erased or destroyed before they could look at it. I don't know who could authorize such a whitewashing of records or why they would authorize it, but I doubt they would do such a thing over a couple weather balloons.
..ok, that it for now but I'll try to add a little more later..