That is the Eero Saarinen building, designated
Terminal 5. It opened in 1963 or 64, maybe as
early as 1962. Not sure. It used to the the
International terminal of TWA. Domestic flights
operated from Terminal 6, next door, a boxy,
glass and concrete building that was vacated
by TWA a few years ago. Today, Terminal 6
serves UA's LAX and SFO flights, American
Trans Air, JetBlue, and America West.
Terminal 5 today is the TWA terminal, it is
also home to Royal Air Maroc, Royal
Jordanian, and Kuwait Airways at JFK. TWA
currently operates 36 daily nonstop flights
out of JFK to Milan, Paris, Lisbon, Cairo,
Tel Aviv (one stop via Cairo to Riyadh),
as well as to LAX, SFO, Seattle, Miami,
New Orleans, San Juan, the Dominican
Republic, and some other domestic US
destinations. Terminal 5 used to be the
airlines Atlantic hub, servicing 747's,
L1011's, and 767-200ER's to Europe
and the Middle East.
Given TWA's financial difficulties, the
Terminal has been neglected for some
time and is in a poor state. It was
designated a landmark years ago.
It was not, however, designed to
accomodate big jets and has had
some modifications to it in the 70's
to handle TWA's 747-100's.