The Kennedy family attracted America because of their glamour and youth. Although JFK didn't accomplish too much in office and made a fool of himself during the Bay of Pigs, he and his family are still remembered favorably-because of their youth and power.
They brought a Hollywood-like feel to the White House, which Jackie made the center of elegance and fashion. JFK was the first young, handsome president, a huge contrast to the typical American president before. Also, JFK's victory as president was significant because he was the first Roman Catholic to be president. JFK's win allowed for more of a variety of presidents to be ushered in.
The Kennedy family is still considered one of America's most powerful and influential families, but they were always trailed by the Kennedy Curse. It's odd that such a successful family loses so many members in freak accidents, but it adds to the interest.