There is a meme out there on blogs and social media about people putting down five or ten RPGs from their teens that influenced them. I chose to go with five. As my teenage years started in the mid 80s, I chose to focus on "my high school years" (1986-1991). The years after that saw a lot of changes in my playing habits, style, and the availability of games that re-defined and hooked me for life.
Advanced Dungeons & Dragons
If you played RPGs in the 80s, you knew or played AD&D, or one of its variants. I did too. Though I will admit not understanding the game early on. I never had the chance or opportunity to learn under a good GM, I had to learn it on-the-fly by myself. Add to it the many problems I saw with the game (limited character choices, multi-classing was the only way to have some basic abilities, and strange rules), especially when comparing it to the other options of this list.
I disliked the game more and more over time, leaving to my completely abandoning it for a decade in 1983 in favor of other games I liked better. It was not until AD&D 3rd that I came back to it and feel in love with it again.
Back in the late 80s, all us Star Wars fans had to go by was the original trilogy (*Amen*) and the Star Wars RPG. The products they came up with were good and much to my own liking. Miles ahead of AD&D IMO. I ran and played in a number of campaigns (I loved playing the retired Imperial Officer template or the Quixotic Jedi). This was a very good game indeed. I often refer back to some of these old adventures for inspiration. Re-reading their plots and twists.
Odd to put here a game whose campaign I just finished. But that is true, I really enjoyed this game back in the day, even if my players' - and my own - grasp of the 19th century warfare was at best very limited. I owe my interest in colonial gaming, which I discovered years later, to this game. In fact, I still own both my original Space 1889 book AND the Soldier's Companion, the minis game that goes with it. I will admit I never played the minis game at the time, but always dreamed of it.
L'Oeil Noir/ The Dark Eye
There is no RPG that influenced me more in the early days than this one. Simple, quick and better balanced than D&D, this game gave you what people griped about vancian magic for years: you had a mana pool and could put it into however many spells you wanted to throw. Even combat was based on balancing your attack and defense points, in a way that is very close to D20 systems today.
However, as much as the rules were fine, the adventures and their plots were really where the game shined bright. It wasn't all to kill the monsters, there was always something else, something more to the story.
Oh the FASERIP system! How I loved you even though you knew nothing of balance. No one ever wanted to play anyone but Thor. Captain America never got any love. Well that's because he couldn't do anything to most of the baddies. It was still a fun system because it had so many of our favorite heroes within. As a big X-men guy myself, I liked to play simpler character, but that was not the case for most players of the time, who had been trained with D&D.
The module were simple and fun, as they departed greatly from the fantasy adventures we had.
I refer to them whenever I want to run something with super heroes.
Now if there is a game that answered my teenage need to destroy things, kill aliens without regards for life, and fire volleys of missiles at random targets, this game had it all. It was also fairly quick and brutal. Although some of my best and earliest campaigns using this system would come during the early 90s with the Macross ][ version of the RPG, this was the one that started things. They had mechs, cool baddies you could kill in droves, loads of missiles, explosions, aliens, big repeating guns, GAAAAAH!. What was not to like about it? I especially liked the Invid Invasion-era game with its "the villains won" feel that still resonates with me today...
I know that's six. So after writing all this, I opted to drop AD&D from this list. It was influential, but in a mostly negative sense during that period.
Did not make the list, because I played but a few short game of it: Warhammer FRP, Palladium Fantasy RPG, Twilight 2000, MERP, and Teenage Mutant Ninja Turtles