One of the more popular conspiracy theories that has been running around for several years (certainly since Oliver Stone's film JFK) is the idea that there may have been some kind of conspiracy regarding President Kennedy's death. Some think that it had something to do with the Italian Mob, some think it was the CIA, some even think members of the government (outside of the CIA) had at least somewhat to do with what happened to him, and most of those who think that there was something fishy about what happened think that there was a second gunman on the infamous grassy knoll.
For a portion of the population, they have a hard time believing that something as significant as the killing of an American president could have been perpetuated by only one man. For these people, the only thing that makes sense to them about the whole thing is if there was some kind of organization behind the killing, an organization that had to go though some sort of planning to make sure that something so dramatic could have happened.
They will point to things like the fact that the president is someone who has all kinds of security around him at all times, and that there are usually all manner of people watching him at all times (ones who are not necessarily involved with keeping him safe, but who are working for him, or who are simply curious about his life); and they will think that because of all of these eyes that are on him, it would make doing something harmful to him as being something exceptionally difficult. And while it is difficult to do something to someone who normally has so many eyes on him, and so many other eyes making sure that there is no one around him who would do him harm, it is not impossible (as proven with President Kennedy, as well as President Reagan).
But the thing with all of these theories that conspiracy buffs have about they think happened is that there are people who have done all kinds of investigations regarding his death (people who have done investigations separately, and who did not necessarily use the same methods or devices to prove their findings), and they have come up with the same conclusions: that Lee Harvey Oswald really was the only shooter who was in Dealey Plaza in November of 1963. They have been able to prove that Oswald was completely capable of making the shots that he did (being a trained sniper with the United States Marines), that he was capable of making it out of the depository where he was shooting from, and that he was able to make it to where he was eventually arrested in the amount of time that was allotted. They have also been able to prove that there was no "magic bullet" that injured both the president and Texas Governor John Connally (because those who claim that it could not have done the things that were attributed to it did not account for the positions that the two men were sitting).
It is completely possible that the reason that some people think that there had to have been some kind of conspiracy involved with his death was because it still seems too impossible for some people that only one man (who quite probably had mental health issues) was capable of doing something so enormous. The Kennedy family (especially at that time) seemed to be larger than life, and in many people's minds, it probably should have taken far more to do any of them any real harm. For them, the conspiracy theories are probably needed, because Oswald proved that only one man could do an immense amount of damage and could have ended (and shattered) lives.