Oh wait, do educational games count? I remember Freddi Fish! Although all I remember is this knot challenge that was really hard :/. I played educational computer games before Pokemon Snap.
If we could go past 2000 I would mention Pokemon Stadium and Paper Mario as big games for me, as well as The Legend of Zelda: The Wind Waker (was 12 when I played it and its probably still my favorite game of all time)