(written from a Production point of view)
Star Trek: The Motion Picture was one of the first games created for the Vectrex Arcade System, a self-contained vector graphics home gaming system. The system included its own game screen (which required plastic overlays to simulate color graphics) and a controller with 360-degree joystick and four control buttons.
The object of this game – a basic "shoot-'em-up" style game for one or two players – was to travel through space and destroy Klingon and Romulan ships. Gameplay had you flying the USS Enterprise through nine space sectors trying to reach the "Klingon Mothership" in Sector 9. Players could control shields and phasers and dock with space stations once per sector to replenish their shields and weapons.
The game was released in the United States in 1982. It was released in 1983 in Europe as Star Ship, and as Harmagedon in Japan. These versions of the game added the additional control of a pause button and the Klingon ships had a more filled out look. Star Trek Debugged  is believed to be a hack of this later version with the title screen suitably altered.
A version of this game was announced for the Atari 2600 but went unreleased. 
The game also was seen in the movie Android, where the character Max 404 was seen playing it.