There's answers to this in the FAQ but hopefully this can add to them.

There is no evidence that the CIA (or any other conspirator) was involved in or assassinated John F. Kennedy. Before we get into the evidence, it's important to step back and understand the psychology of grand conspiracy theorists. I say "grand" conspiracy theorists because conspiracies do happen. When two or more people "conspire" to commit a crime, it is, by definition, a conspiracy. Sometimes conspiracies exist in the United States to overthrow leaders or otherwise disrupt power structures. Abraham Lincoln was assassinated as part of a conspiracy; Secretary of State Seward was gravely wounded as part of that conspiracy.

Grand conspiracies are those massive cover ups that we've heard rumors and whispers about, perhaps even to the point of plausibility. Did the U.S. really land a man on the moon (yes, we did). Were the attacks of September 11, 2001, orchestrated by the government (no, they weren't). When these theories are presented, they can initially sound impressive—jet fuel doesn't melt steel, Jack Ruby had mob connections, etc. We evolved as a species to often accept the first information presented to us, then discount information that follows that contradicts it. So if someone hears something new, it sounds impressive. Also, being "in the know" of a conspiracy can give one a sense of belonging to a community and superiority.

But upon closer examination of grand conspiracies, they require far-fetched ideas about human nature, government, bureaucracy, and so much more. Once it's suggested, for example, that the CIA killed Kennedy or was involved, what does that really mean for how the US government operates? For such conspiracies to work, there has to be a shadow apparatus behind essentially everything that happens in the nation. And that's why grand conspiracy theories grow even grander and it's why so many of their adherents often sound extreme to the point of unhinged. Kennedy wasn't just killed as the result of a conspiracy; he was killed, his brain was removed and replaced with another person's, the autopsy was covered up, Oswald was a patsy, Jack Ruby was brought in, umbrella man, the grassy knoll...on and on it goes. And that is a fraction of the theories in the Kennedy assassination. Three "tramps" (I'm using the term they're known by in the conspiracy community) were spotted outside the Book Depository building on the day of the assassination. Who were they? What happened to them? These kinds of anomalies feed the conspiracy fire. (The homeless men's names were disclosed about 20 years ago.)

It was Vincent Bugliosi who wrote that these anomalies "don't go anywhere." Let's say a witness swears she heard four shots instead of three and she thinks one might've come from the grassy knoll. Okay...then what? What follows after that? How does that tie into Oswald and his actions that day (explained below) and what else we know about the assassination. What follows from these anomalies relies on such a tortured explanation, to the point of misrepresentation, of the known facts, that you have to end up with a vast conspiracy populated by literally hundreds, if not thousands of people, at the highest levels of world government. Believing in these grand conspiracies, in other words, requires a paranoid, fantastical view of everything we know about the world.

An important point of conspiracy thinking is that everything becomes evidence for the conspiracy. If there's an anomaly (as there are in all murder cases, let alone a high-profile one), then it's evidence of a conspiracy. If there's some unexplained event, it's evidence for a conspiracy. But it works the other way, too: if there's evidence that there *wasn't* a conspiracy, well that's just part of the conspiracy trying to cover itself up. If new evidence emerges discounting the theory, then that's because people (usually conspiracy buffs) were getting too close to the truth and the conspirators had to come out of the shadows to misdirect. Nothing, in other words, can ever actually be seen as proof against a conspiracy. And, of course, anyone can say anything; it takes a sentence or two to assert that there was a conspiracy, but it takes reams of paper to analyze and attempt to disprove a conspiracy.

Finally, before we get into some of the specifics of the Kennedy assassination, conspiracy theorists are so accustomed to discounting any official narrative or explanation, it becomes impossible to use those narratives to dismiss a conspiracy. This is particularly problematic with the Kennedy assassination because the Warren Commission actually did a decent job, and their investigation provided most of what we know about what happened that day. They produced a volume explaining the assassination and then over two-dozen volumes detailing their research, investigation, and evidence. But the notion that the Commission did a lousy job has become so commonplace that even people who don't believe in a conspiracy accept it as gospel. No investigation is perfect, and the Warren Commission and the FBI made some mistakes, but none that call their conclusions into question. 1/3