As far as individual reverence goes, I think that many people who were alive that day remember much in way of "Where were you on November 22, 1963?" This question is something where an immediate answer can be given. For those who were aware of it, the moment when they heard "the President's been shot," is one of those moments that caused individual recollection to be triggered. Indeed, the moment itself could be construed as a moment where "things changed," making it more than just another moment and actually a historically bound one. However, I think that the personalized nature of it in terms of it being a significant instant with a sitting President being shot and the confusion that resulted afterwards have combined with individual narrative to become a moment that is rare and unique. I think that in addition to this would be the very idea that the moment itself has become historically driven with the fervent study of the assassination, itself, and whether or not there was a conspiracy to kill the President. It's a rare moment. Individual narrative, secondary historical analysis, as well as the primary focus of a sitting president being assassinated helped to make it one of those moments where it is "different" than others. It might not be one of those moments that changed history (although it has been argued as such), but rather is a moment where a variety of circumstances and conditions converge upon it.
I also tend to come down on the side of JFK's assassination not being a true turning point in history. His successor was also a pro-civil rights, cold warrior from the same political party. It did not have a significant effect on the economy of the country when he was killed, and his family's political dynasty was far from finished. The Space and Arms Races continued unabated under Johnson and Nixon.
That being said, I agree with the above posts historical points about Vietnam and Civil Rights. I also don't know that JFK would have pursued Great Society programs like Medicare and the War on Poverty, at least to the extent that President Johnson was able to. I might also be able to argue that JFK's murder took away an idol and hope of the younger generation that the 1960 election and JFK had energized. The counterculture backlash against the government and Vietnam was perhaps stronger because of his death.
Personally, I think it was just another event in history and I think that this point of view will come to dominate as we get farther in time from the event. I think that recent historians have been emotionally connected to the JFK years and so they give the assassination more attention than it warrants.
However, if I had to make an argument saying that it was a turning point, I would say that it led to two major things -- the escalation of the Vietnam War and the civil rights advances of the 1960s. I would say that his death led to these things because it put Lyndon Johnson in the White House.
I would argue that Johnson escalated the war where JFK would not have. I would argue that Johnson's personality was much less flexible than JFK's and that he was much more likely to do something like using the Gulf of Tonkin incident to increase US troop strength.
Then I would argue that LBJ got the civil rights bills of 1964 and '65 through Congress when JFK would not have been able to. LBJ was a great legislative tacitician and knew how to get bills through. He also could use JFK's name as a way to get support -- the idea that they had to push these things through to honor JFK.
Having lived through this trajedy, I believe that people in that time period thought that JFK was a symbol of what was right and good in America. After this assassination, the country realized that no one was "above" the base rules of craziness in the world.
If it was just another event in history, why are there so many people who still believe that there were conspiracies surrounding it? It did lead to the escalation of the Viet Nam war, but that was another turning point that stemmed from the assassination, it wasn't just another event in history.