I was always really pleased with my quick 'n dirty D6 System conversion of Task Force Games' 'Prime Directive' core rulebook, that even used the book's own system and character sheet. It can be found in the free section of my website http://www.farsightgames.com/. It was simple and yet effective and, even though you'll need to locate extra rulebooks that are very old and out of print, it worked well.
This brings me to the original FASA game from waaaaaaay back in the midst of time, when hairspray was abundant and 18th century clothing and a white stripe across the nosebridge was the 'in' thing. Of course, I'm talking about the early 1980s.
The copy I have is the Games Workshop Second Edition printing. It was a great little system, percentile based, and the characters you could create were given depth by having them develop through applying to Star Fleet, going through Academy training and then active service. The final character was fleshed out and easy to play, and whilst the damage of weapons of the era (the Original Series) was slightly over the top (one hit disintegrations!) the system was pretty fluid and fun.
I created a character for this back in 1989 but never played him. I might give this game a stab at some point.