JFK was ahead of his time on civil rights, as he addressed the entire nation and called them out on segregation and how blacks were treated in this country. Like Truman before him, JFK was a new kind of Democrat, and this was the beginning of the split between the South and the Democratic Party. Today, ironically, they have switched over to support the party of Lincoln. JFK is most remembered, as mentioned above, for his foreign policy successes in the Cold War.
JFK inspired people. He made the presidency cool again. I know this might not be what you are looking for, but I do think it's important. He may not have actually accomplished much, and his biggest failure was getting killed, but he did leave a lasting impression. He also gave us a hero or martyr president.
The most obvious successes and failures of the JFK administration were to be seen in foreign policy.
The most high-profile and obvious failure was the Bay of Pigs Invasion. In this incident, the US clearly failed to bring off the invasion of Cuba that it was supporting. This made JFK look weak because he allowed the invasion but failed to support it enough to make it work. Although we did not know it at the time, another failure (one can argue) was JFK's policy towards Vietnam. It was during this time that the US got more deeply involved in that conflict.
The major success was the Cuban Missile Crisis. This incident made JFK look much more effectual than he had the year before in the Bay of Pigs incident. Here, JFK's leadership prevented nuclear war and also made the USSR back down. This was the major foreign policy success of JFK's time in office.