Amarillo Design Bureau offers GURPS Prime Directive, which is close to a Star Trek game. It's set in their "Star Fleet Battles" universe, which is a sort of "alternate world" of The Original Series where all the species from the old series, and some new ones they invented or borrowed, got into a galactic war at some point.
If you like your Klingon's smooth-headed and your female Starfleet officers in mini-skirts, that's one way to go.
"On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
- Charles Babbage (1791 - 1871)