Simple, he got shot. America tends to make martyrs out of everyday people. I truly believe that had he not been shot, he and the rest of the "Kennedy Dynasty" would be in the dust bin of history. Had Teddy not been a Kennedy, and had his brothers (plural) not been shot, he would probably be in jail.
It's the movie star angle -- young and good looking and famous for being famous. What did his son do to become so famous in his own day? It's the same created aura that makes people care about Jennifer Anniston or Julia Roberts or Russell Crowe or someone called "Colin Farrell." Kennedy's popularity is an example of the hidden monarchism that lurks beneath the surface of mass society.
Plus, Kennedy's a figure on whom people can pin the leftist hopes of their youth. In Europe, it's the radicalism of 1968 that performs the same function. Democrats who "believe in government" need to have someone in government to believe in and attach their hopes to. So a mystique grows up. Curiously, even some people who were old -- or not yet born -- during Kennedy's lifetime do this.