Would the 1960s have unfolded in substantially different ways had President Kennedy not been assassinated?
This decade would have unfolded a great deal differently had it not been for this assassination. This would most have been true about domestic politics.
In the domestic sphere, Lyndon Johnson's presidency is known for civil rights laws and the "Great Society." It is likely that Kennedy would never have gotten either of these kinds of laws through Congress. Kennedy had no real legislative skills while Johnson was a master. Johnson also had the advantage of the fact that people felt they needed to honor Kennedy's memory by supporting things he advocated.
Had Kennedy not been killed, there might not have been the Civil Rights Act of 1964 and there might not have been the Great Society. This would have radically altered the history of the '60s.