A couple games, that shaped me in different capacities and ways. Obviously, all pretty old by now and a long time ago, and I mentioned them and how they impacted me in the Top 50 thread.
Duck Hunt (NES): Likely the first video game I ever played, played a lot with my cousin at my aunt's house, an avid gamer at the time while I just wanted to go to the playground instead.
Soccer (NES): Another game I played a lot with my cousin, opened me up to competitive gaming.
The Legend of Zelda: A Link to the Past (SNES): The intro to this game, where it rains outside, made a lasting impact on me and is thus one of the most influential games on my personality. The intro was the most epic thing I ever saw at the time, and instantly made me a gamer, and Zelda my favourite series for the rest of my life. If my aunt hadn't shown me this game, I wouldn't be gaming, in any capacity more than a casual one, today. Maybe I'd even have played sports, can you imagine.
#14: Gunfighter (Showdown in 2100AD) (G7000/Odyssey2): Simple arcade game on an old 2nd Gen console my mother dug up from the attic, made me appreciate there were more manufacturers and more types of games out there, this broadened my horizon.
Star Wars Rebel Assault 2 (Mac): My introduction to Star Wars and the first game I played on a home computer, after my new stepfather bought our house our first computer. Star Wars would become my favourite media franchise, and I watched the movies and everything else because of it soon after.
Step-On-It (Mac): Obscure puzzle game from an obscure developer on Mac computers, a clone of the NES's Solomon's Key. The game made me appreciate challenging, puzzle and problem-solving oriented games, pushing towards certain genres and series in later life.
SimCity 2000 & SimTower (Mac): Played simultaneously and had a cumulative and severe impact on the course of my life. These games, with SimCity 2000 later being replaced by 3000 and 4 on Windows PCs after it, sparked my interest in architecture, city building and construction in general. This made it so I went on to study architecture later in life, and become an architect. These games had the biggest impact on the course of my life of any, and I wonder how my life had gone, and what I would be doing now, if I never played SimCity and SimTower.
Mario Kart 64 (N64): This game has a lot of emotion attached to it and probably has the most memorable play session of all time for me, because it was the last game I played together with all my family, until drama and worse made it so most of those I played with aren't around anymore for various reasons.
Anno 1602 (PC): I played this, and still play the game's successors with my best friend, and while our friendship was already long and strong as it started on the first day of school, this game probably cemented it for life.