Well that's one of them alright!
I can't remember the first game I played, but I know Tetris, Metroid, Donkey Kong, Earthworm Jim, and Sonic 2 are probably among the first games I played. I also have fond memory of those "100 games in 1" cartridges, I played the hell out of 'Tank'.
Final Fantasy 7 and Ocarina of Time were my first major games I guess.
On the PC, I think it was C&C Red Alert, but since I was so young (and dumb), I remember messing around with the .ini files making my units overpowered, because I had no clue as to what I was doing. Earth 2140 was a great strategy game too, I actually played that one properly.
This. Hence not remembering any of the names.
But some of the ones I do remember the names include bomberman (might have been later actually), Mario, Ice Climbers and stuff like that. There were some racing games and other stuff too but i don't know the names.
First RPG I finished was Tales of Destiny. FF7 I didn't manage to get that far, FF8 (much later) I was at the last dungeon but computer got reformatted along with my save.
On PC the oldest... I do wonder. It was on DOS.
Oh and a tank game you can play 2 players. That one was fun :D