Well, it may be off-topic, but it was an interesting discussion to read all the same!
Anyway, to answer the original topic, I remember looking over my brother's shoulder as he played our new Game Boy we got for Christmas. He was playing both Super Mario Land and then TMNT: Back from the Sewers, I think is what that was called. I know I was, like, "When can I play?" in my cute 4-year-old voice.
Some of my favorite moments that Nintendo helped shape were playing Pokemon for the first time in middle school, being totally addicted to it, buying all the toys, buying all the cards, recording every episode of the anime, and drawing my own fan-fiction comic books.
I remember arriving with my mom early in the morning for both the GameCube and Wii launches. The GameCube one was a cold November morning on a Sunday, and it was raining outside the Toys 'R Us. As for the Wii, it was a much easier experience. We waited in line at Target for about an hour, and then we got a ticket ensuring us of getting the system. All we had to do was come back in an hour to pick it up and select our games. We got six games, not including Wii Sports. It was a magical occasion for both launches.