Star Trek II: The Wrath of Khan Released June 4, 1982.
It's not an exaggeration to say that without Khan, the franchise likely would have died. The first Trek film, 1979's Star Trek: The Motion Picture, made money, but it was ponderous and abstract Gene Roddenberry seemed to be trying to blend the cerebral 2001: A Space Odyssey with the lithe Star Wars. By contrast, Khan (on which Roddenberry was merely a consultant) had a stronger sense of the original series' core identity: a show about an impulsive badass and the logical best friend who always tries to restrain him. Spock's spectacular self-sacrifice at the end of Khan sets up a long, vital story arc that hurtles Kirk toward maturity and ultimately leads the Federation to peace with the Klingons. Without that peace, the franchise never would have been ready for The Next Generation, the series that led Trek to the pinnacle of its popularity. A bit of trivia: Both the new Trek film and the previous one (2002's not-as-horrible-as-everyone-says Star Trek: Nemesis) borrow heavily from Khan. The new film, for instance, explains the origins of Starfleet's famous Kobayashi Maru test, first introduced when a very young Kirstie Alley fails it in the opening scene of Khan.