One of the first games I ever played (well, the first has to be an Atari one, but I can't remember which one. Probably Montezuma's Revenge). My cousins had a NES with SMB/Duck Hunt and whenever I went to their house, they never let me play. I just had to watch.
So in Christmas '93 (or was it my birthday? They're both in december, anyway) I was surprised when my parents got me a SNES with Super Mario World. Jaw on the floor and all. Probably behaved like that NINTENDO SIXTY FOOOOOOOUR kid, I can't really remember.
Thing is, it became MY game. It was the only one I had, of course, but Mario became my companion. in a way. And instead of making me addicted to it and turning me away from my family, it bonded us for a while. My parents played with me from time to time: I spent most of the time with my mom during the day, so obviously she watched me play the game a lot and tried to help me as best as she could. My dad helped me with english and helped me translate some of the words I didn't understand. In a way, not only SMW began my appreciation of videogames, it also made me start learning english by myself.
So yeah, it's arguably the most important game I've ever played. And even if there are better games, bigger, brighter, more difficult, even more memorable and influential... this one will forever have a place in my heart.