For me, it was Super Mario All Stars. I would always go over my cousins house and they always had the newest consoles. Whenever they got burned out from playing Super Mario RPG or Mario Kart 64, they'd let me play the SNES. I would get to 1-2 and die there all the time. I was like...3 or 4 years old.
My first vivid memory was Super Mario Bros. Deluxe on Gameboy Color. I played the heck out of that game. I just wanna say thanks to Nintendo for creating such a great and timeless character. My life would be significantly different without them. Thanks!