Star Trek - script game - happened in 1972.
Star Trek - text game - was created in 1971.
Star Trek - arcade game - was created in 1982.
Star Trek - text game - happened in 1971.
Star Trek - arcade game - happened in 2600.
Star Trek Roleplaying Game - Decipher - happened in 2002.
Your question is too generic - how do you beat what in what Star Trek? Are you asking how to beat a specific video game incarnation of a Star Trek product?
Release date of Star Trek Armada is February 29, 2000. Star Trek Armada is a RTS video game from Activision.
Yes, Star Trek was a category on Jeopardy on December 17th, 2007.
Star Trek Online is now free to play and does not require a subscription or to be unlocked. You can download the game at arcgames.com
Most stores that have video games will stock Star Trek games. Amazon and Game Stop both have Star Trek games in stock, but they generally did not receive positive reviews.
The game can be downloaded for free from the Perfect World website.