For my early youth, most of the Sega Megadrive games. Steets of Rage, Sonic the Hedgehog 1/2, Altered Beast... Mario 3 on the SNES stands out too.
I think when I was about 8-9 my cousin actually gave me Final Fantasy VII for the PS1 because he just didn't like it. It's been one of my favourite games ever since...though I didn't get out of Midgar until I was about 13. I actually thought Rufus would be the end boss.
EDIT: Oh, and TMNT4: Turtles in Time. I actually got this at a second hand store selling American games...I needed an adaptor for it, but damn it was one of my most played.