That's one really weird poll.
Anyway, my first was the N64 one. I both learned about it and played it for the first time while visiting some cousins and instantly fell in love with the game. A while later, after moving to a different city, I made some new friends and one of them happened to have the game, we had a lot of fun times with that thing.
I later got an N64 of my own, Smash was one of my first games. Though I don't have the cartridge any more, shame.
Melee? I didn't get a Gamecube until 2005 and I didn't have many chances of playing on one before then, as most of my friends played more on Play Station or PCs so they didn't have one. The only times I actually played Gamecube games before that was when visiting my cousin, which didn't happen all that often (and we played a lot more games than Smash too, so my time with it was very limited), so yeah, I only really got into Melee from 2005 onwards.
Then I finally got Brawl day one, same with Smash 4.