Star Fox 64! My older brother would never let me play, but whenever he was at school I would sneak into his room and spend hours playing it. Such an awesome game.
Either Mario Kart 64 or the origin Super Smash Bros. They are both great games. Mario Kart 64 was definitely the first game my brother bought, but I'm not sure if that is the first game I played.
Mine was probably... Lego Racers. **** straight. It was a pretty BA game, and me and my brothers played it for hours. I remember it real well, usually just screwing around, but i was little then.
When i saw this post right away i thought it meant like what was the first video game ever, so i was thinking about my NES. Yeah, a BA, mint condition, NES. And i have the REAL, FIRST, Mario game. It also has duck hunting on the cartridge. Pretty sweet.