It wasn't so much the game, but the NES that got me introduced to gaming. Along with the Super Mario Bros/Duck Hunt game, a arcade TMNT game, and a football game that took place between '96-'98 cause the Cleveland football team was named the Crunchies since Art had taken the Browns to Baltimore, I got my first taste of gaming then.
Pokemon helped me get into handheld gaming, and Silver launched me into the Gameboy Color years...but the game that got me hooked has to be Paper Mario. Not playing it, cause I only got to experience it from the spectator's chair at a friend/neighbor's house. But wanting to play it, my parents got me and my sister the Gamecube, and from then on I've been a gamer. From Luigi's Mansion starting it off, to me now owning almost 200 games across multiple systems, and the last game I recently (re)played (starting my 3rd play through) being Deus Ex:HR, if it wasn't for that desire to play Paper Mario, I don't think I would have had the push to get the system and find my love of gaming