Earthbound, and to a much lesser degree Super Mario RPG.  The games that cemented my love of my favorite genre.  Not sure if I was 6 or 7 when I first played Earthbound, may have been slightly older. 

Spyro, crash bandicoot, and final fantasy 7 from my really really early days, and grand theft auto 3 from my early days.

has to be smash TV, best game, with super mario world a close second.

Xenogears

Secret of Mana

Chrono Trigger

Final Fantasy Legends 2

Final Fantasy IV

these were my early addictions as a lil kid:

- super mario bros 3
- sonic 2
- return to castle wolfenstein (and ppl say kids play violent games nowadays....pssh.... hot dog!!!)
- king's quest 5. so awesome

My childhood was on the early Atari like Space Invaders, and then with nintendo with their marios and zeldas but i've not loved playing games until i got a Sega Genesis , i've always bought very niche japanese games for it , they were awesome (even though i've still to this day never understood them) , this trend continued when the PS1 released, which has become my favorite platform, more niche games = more awesomeness.

Pokemon Blue/Red/Gold/Silver, Super Smash Bros Melee and Zelda WW were the definitive games of my childhood

Final Fantasy I, Dragon Warrior, Crystallis, Sonic the Hedgehog, Super Mario Bros 3, Virtua Racing FX, Adventure Island, Pokemon Red&Pokemon Gold....the list goes on.

PS:

Crash Bandicoot 1, 2, 3, Bash and Racing

Metal Gear Solid

FF VII and FF VIII

Gran Turismo

N64:

Super Mario 64

Donkey Kong 64

Pokemon Snap

Gameboy:

Pokemon Red/Blue/Yellow and TCG. I had them all!

My old time favourite games are Super Street Fighter 2 Turbo (Arcade, PC and SNES), and Sensible World of Soccer and Cannon Fodder on the Amiga. Good times!