The "Take Me to Havana!" airline hijackings, were a major political, security and trasportaion issue in U.S.–Cuba Relations in the late 1960s and early 1970s. The fist was in 1958 and the last was in 2007, but it peaked between 1968 and 1972.
These incidents were attributed to terrorism, extortion, flight for political asylum, mental illness and (mostly forcible) transportation between the two countries.
An American man and woman, hijacked a DC-8 from New York to Cuba on January 2nd, 1969. The man was killed while the woman is still an unapprehended fugitive.