I started with Combat on Atari. it was nice because it was 20 games in one. I didnt play Atari much because the games stunk.
I played alot of arcade games starting in '82. Williams games were my favorites. Robotron 2084 would be my most influential game.
twin sticks is still the standard control scheme for top down shooters and FPS on console. now that's influential.
Gauntlet is another game that was pretty influential. a lot of isometric dungeon crawlers are iterations of the classic.
Myth: the Fallen Lords was ahead of its time and pretty influential. I'm reminded of Myth: TFL every time I play Total War Warhammer