While the Kennedy assassination has taken on a life of its own as a conspiracy topic (for a variety of reasons), there have been many other historical events with challenges to the accepted narrative, including those related to groups like the Illuminati and the Freemasons. As for specific examples, though, I'll give you three below to start.
The Lincoln assassination - While the Booth conspiracy came to be accepted quickly as correct, there have been many other versions, including that Jefferson Davis knew of the original Lincoln kidnapping plot, that eventually turned into the assassination. Another theory that had a number of proponents had Secretary of War Edwin Stanton behind the conspiracy, mostly to keep Lincoln from being too lenient on the Confederate states during Reconstruction. Here's a good rundown on some of these: Lincoln Theories.
Warren Harding - When Harding died suddenly, there were whisperings that his wife was behind his death because of his philandering. Here's a brief review of some of these ideas: Strange Death.
Pearl Harbor - The idea of FDR having foreknowledge of the attack was not unusual, even during World War 2. There were politicians and others who saw it as Roosevelt's way to get the United States into the war (somewhat similar to those who felt that Lincoln "allowed" the attack on Fort Sumter to happen to get the Confederacy to fire the first shot).
These theories have a number of things in common with the JFK event, in that information was either kept secret or covered up that tended to fan the flames of conspiracy, rather than reduce the speculation. Even now the Pearl Harbor conspiracy theory appears off and on. From all my research, whether JFK was killed by a lone gunman or as part of a conspiracy, the actions of various organizations has helped keep the story popular. While Philip Shenon is definitely on the lone gunman side, his book on the Warren Commission investigation, "A Cruel and Shocking Act", definitely shows how the CIA, the FBI, and other groups purposely misled the commission, which has contributed to the continuing belief of a conspiracy. This is similar to the Harding example, where his wife would not allow an autopsy. In addition, the Warren Commission itself didn't help, since much of their work smacked of a "political" solution to a crime. I obviously just scratched the surface, but the conspiracy theorist has pretty much always been with us!