The Kennedys were very close to the Mafia because of their father's old connections. Sam Giancana in particular, as I recall.
The connection between JFK and Giancana was Judith Exner:
http://en.wikipedia.org/wiki/Judith_Exner
Sam Giancana was also the inspiration for the horse's head scene in the Godfather film, Giancana Vegas casino money having partially financed several of the early films in which Marilyn appeared after her contract with Fox Studios was not renewed in August 1947. Then, in December of 1950, she got a new contract with Fox....