When I was 6 years old, I only had Super Mario 64, Top Gear Rally, and I thought I had Hexen by that time too.
That's all on the Nintendo 64.
I also had floppies of Super Mario Bros., Donkey Kong, and Keen for MS-DOS.
I've never played games before being 6 years old (I didn't even know such things even exist).
I never really played any video games when I was like, 6 or younger, except maybe a few Game Boy games like Pirates of the Caribbean and Arcade Advanced. But 3rd grade is where the childhood games began. Super Mario Sunshine, Mario Golf Toadstool Tour, Luigi's Mansion, they all bring back the memories.
I was more of a Pokemon guy when I was younger. During the late '90s, there was that massive Pokemon craze of course that influenced me as a little kid. The most memorable Pokemon games for me were Yellow, Gold/Silver/Crystal. However, I did grow up with a few Mario titles (mostly Super Mario Bros., Mario 64, and a few Mario advance games).
Well I they may seem a bit too modern, but since I was born in 99, ya know. My child games are Super Smash Bros. Melee, Super Mario Sunshine, Luigi's Mansion, Soul Calibur II, Crash Bandicoot 2, Crash Bandicoot: Warped, Pokemon Channel, Pokemon Colosseum, Wario Land 4, and Wario World. :D
Donkey Kong Country (SNES)
Super Smash Bros. (N64)
Yoshi's Island (SNES)
Game & Watch Gallery 3 (GBC)
Super Mario Land 2 (GB)
Harvest Moon 64 (I played this more than probably anything when I was little) (N64)
Super Mario All Stars (SNES)
Toy Story 2 (N64)
Donkey Kong 64 (N64)
My brother hardly ever let me play his Game Boy at this time, so I have few of those as childhood games.