Sci-fi TV shows and movies with spin-off novels, comic books, and games, in a setting originally devised by Gene Roddenberry.
Several licensed SF RPGs have been set in the Star Trek universe, from companies such as Heritage Models, Terra Games Company, FASA, Tsukuda Hobby, Last Unicorn Games, and Decipher. There have even been two free Star Trek RPGs released on PDF, Far Trek and Where No Man Has Gone Before.
There are also games set in the Star Fleet Universe setting, an alternate universe in which history diverged after the events in the original series. These include the Star Fleet Battles wargame and a roleplaying game called Prime Directive. The RPG was first released with a unique game system, and then converted to GURPS, d20, and d20 Modern.
Those wishing to use GURPS to roleplay in the canonical Star Trek universe can easily adapt GURPS Prime Directive, since that setting is very similar. There have also been various fan-created GURPS Star Trek adaptations circulated online, and GURPS Spaceships can be used for starship combat.