Star Trek roleplaying game (or, rather, there was, but I had never seen it). However, there was a wargame set in what appeared to me to be the Star Trek universe called Starfleet Battles and it intrigued me greatly.
The earliest version of Starfleet Battles was released in 1979 and was designed by Stephen V. Cole. It was sold in a zip-lock bag by Task Force Games, making it a "microgame" similar to Ogre or Car Wars. A boxed "Designer's Edition" came out in 1980 and was a much more impressive -- and complex -- game than the original. I owned the Designer's Edition, but I never played it, whereas I actually did play the microgame version several times at local gamer gatherings at public libraries and similar locales, even though I never owned it myself. If anyone knows me, this fact alone should tell you all you need to know about the differences between the two versions of the game.
The 1979 version wasn't intimidating to my 10 year-old self; I picked up its rules quickly and had a lot of fun engaging in starship battles between the United Federation of Planets and the Klingon Empire. That's not to say that the original Starfleet Battles was simple, but it was still simpler than the game it would become as early as the Designer's Edition published just a year later. Its movement system, for example, required some getting used to, since it was impulse-based. Likewise, keeping track of a starship's energy allocation could be tricky, even with the forms that came with the game. I suspect, though, that my abiding love for Star Trek is what enabled me to barrel through the game's nuances in order to be able to play it, a love I did not possess for, say, World War II. Without such affection, I doubt I'd be able to say, in truth, that I'd ever played Starfleet Battles.
The other thing that drew me to this wargame and held my attention was the fact that it appeared at a time when there was little else to sate the appetite of a Star Trek fan who wanted more. Hard though it is to imagine in 2011, Star Trek was not a juggernaut of global marketing in the late 70s. We had only the Original Series, the Animated Series, and a handful of books and fanzines to draw upon. One of those books was the Starfleet Technical Manual by Franz Joseph, who'd also produced a series of blueprints to many of the starships seen in the Original Series. I owned the Technical Manual and adored it, so the fact that Starfleet Battles drew heavily from it was, to me, proof that this wargame was a gift from heaven for a young fan like myself.
Others better versed in history can explain the full details, but, as I understand it, Task Force Games produced Starfleet Battles under a liberal and open-ended license that gave them full access to the Star Trek universe as it existed at the time of its 1979 publication. This means that the Original and Animated Series are both fair game, as are books like the Technical Manual, but nothing in the subsequent films or spin-off series is available. Consequently, Starfleet Battles is said to take place in "the Starfleet Universe," which is a kind of alternate Star Trek universe. Inevitably, this alternate universe, as the setting for a series of wargames, is rather militaristic in overall feel. As a kid, this never bothered me much and, even now, I can't say I find it particularly problematic, but some Trek fans intensely dislike it and see it as a "betrayal" of Roddenberry's vision of the future.
As I said, I owned the 1980 boxed set but never actually played it, in part because its rules were longer and more complex, but also because, in terms of presentation, they just felt a lot more intimidating. Though the microgame version of the game was every bit the wargame that its successor was, it somehow felt more inviting to me and so I was willing to learn how to play it. The 1980 edition instead just gathered dust on my shelf. Eventually, I raided its collection of counters for additional starship markers to use with FASA's RPG. In the years since, I haven't had any particular desire to go back and try to play Starfleet Battles, though the recent news that there may be a RPG version of Starfleet Battles using the Mongoose Traveller rules has made me think about pulling the game off the shelf and giving it another look. A pity I can't find a copy of the 1979 rules; I might actually try to play that version.