My first Star Trek campaign started in late 1982 when I acquired a copy of the first edition rules for the FASA Star Trek Role-Playing Game. I had played (and enjoyed) Traveller, but had come to the realisation early on that it was ill-suited for a Star Trek campaign. FASA's game had what it takes. It was a Stat'n'Skill game like Traveller and unlike D&D. It also had a great lifepath generation, giving each character a full backstory. It was also associated with a very nice line of figures and ship miniatures.
I immediately came up with a ship and a history for it. I would use the USS Excalibur, NCC-1705, which had been severely damaged in the M5 incident. I figured that Starfleet might refit this ship the same way it had the Enterprise. Its captain was an NPC, Captain Eugene Stephen Roquefort (called "The Big Cheese" by his crew, who had been a lowly Lieutenant during the M5 battle and was one of the very few to survive. Now, he was in command. I ran several adventures for a gaming group in Halifax, eventually moving away in 1985. In Ottawa, I resumed the game with some new friends, and a couple of old friends who'd also made the move. In 1988 or 1989 I put up a poster in the local Hobby store looking for players. I got a call from a guy who said he was part of a group looking for a new GM. They already had characters and some NPCs. This was just what I'd been hoping for! The three guys in the group have been close friends of mine ever since. They followed me across town when I moved again, and it was several years before one of them moved away. After that the group sort of dissolved. By then they were all highly-ranked officers; had gotten a new-build ship, the USS ExcaliburNCC-1705-A; and we'd outgrown the FASA game, going to a home-brew based on GDW's "House" system.
Fast-forward four or five years... I got a call saying Bruce was back in town and Steve was willing to commute once a month, and would I be willing to start the game back up? As it happened, I was. I had just got the ICON system and was working on the Relic campaign, so I started them all over again as junior officers. And the rest is history...
using the Star Trek: The Role Playing Game® rules by FASA Corp.