There have been four role-playing games released for the Star Trek universe. The first (which came out in 2 editions) was by the now defunct FASA Corp. The FASA game used a "d%" system, where all attributes and skills were expressed as percentages. FASA also released several adventures for the game, most of which were excellently written.

The FASA version of the game was also supported by a starship design and combat game called "Star Trek Starship Combat Simulator". All told, the FASA effort was superb. Unfortunately, Paramount and Gene Roddenberry thought the game was not politically correct enough.  In any case, Paramount pulled the license in 1985 and the game sadly went out of print. Nevertheless, it was one of the best role-playing games I've seen in a long time and it simulated the Trek universe pretty well.

There was an unofficial GURPS version of Star Trek and a more official version based on ADB's Star Fleet Battles called GURPS: Prime Directive. The Star Fleet Battles universe is based on the 1979 Starfleet Technical Manual by Franz Joseph Schnaubelt.

Franz Joseph Schnaubelt was a true Trekker and knowing that the series wouldn't continue (at least not so soon), he carefully supplemented the information on screen with his own creations, such as the Articles of the Federation, flags and emblems of member worlds, a design for an orbital Starfleet Headquarters and his famous starships. This is where some sort of dispute is going on. Especially many older fans still regard the Star Fleet Technical Manual as canon, considering that Franz Joseph had Gene Roddenberry's support on it. Some time prior to TNG, they had a falling out, and it is said that Roddenberry intentionally laid out technical specifications of TNG so as to devalue Franz Joseph's work - this is probably part of the generally leftward drift of Roddenberry's socio-political viewpoint that went on later in his life.  Personally, I find Franz Joseph's work to be of uniformly high quality and while parts of the Technical Manual have been contradicted by later Trek, a good deal of it has not. Some parts, like the Articles of Federation, enjoy almost universal fan acceptance.

In 1996, Paramount awarded the Star Trek RPG license to Last Unicorn Games. Last Unicorn (or LUG for short) turned out an excellent and well-supported game with extremely high production values. The game itself used a new engine called the "Icon System". While it represented the Trek universe relatively well, I never could keep the task resolution engine straight.

In 2000, Wizards of the Coast bought Last Unicorn but Paramount had PC issues with D&D so it pulled the license again, re-awarding it to Decipher. Decipher is better known for it's CCG's. It was (and still is) the producer of the Star Trek CCG (which is actually not bad... and as someone who HATES CCGs, that's a rave). Decipher promptly hired the entire LUG team (and then fired them again in late 2003). They used a system that bore more than a passing resemblance to the Traveller system. Which I guess isn't surprising since Mark Miller served as a technical consultant to Decipher during the redevelopment of the game. The Decipher game was pretty good but it is not nearly as well supported as the LUG game was. Fortunately, the two are similar enough that translating from one to the other is not difficult. Decipher declined to renew their license for Star Trek RPG in 2007 citing poor sales, the game went out of print in December 2007.