I had A LOT of favorite games growing up...
I played mario brothers on the original NES as a very young child, it was probably my favorite at that time, for some reason the other NES games just didn't do it for me... I was raised on horror movies, mom claims we watched Halloween for my first time when I was 2... So I was very, very, very disappointed that the friday the 13th game sucked so fuckin' much.
When we got the super nintendo, super mario world was absolutely my favorite!
From probably 96 - 2000, I was addicted to pokemon on gameboy haha. Had pokemon red
Nintendo 64 I'm not real sure... PROBABLY castlevania 64, but possibly Legend of Zelda Ocarina of TIme... I personally liked Zelda more, but mom didn't like it so we always played castlevania, which made it a little more special for me lol.
Even though playstation came out in '95, I really didn't even hear of it until 2000, right before the PS2 came out. Got one at a garage sale along with some games, soul reaver was one of my favorite and it's STILL one of my favorites. But my ALL TIME favorite PS1 Game was and is The Legend of Dragoon!
I got the ps2 on August of 2000, on my birthday haha remember it like yesterday! I'd have to say that Orphen: Scion of Sorcery was my favorite game on PS2, as it was the first game I got for it and was still replaying it when ps3 came out - However, the other Legacy of Kain games were close runners.
I never really cared for the gamecube.
And that pretty much ends child-hood... Nothing but teen years from then on out lol, which included the fable games, elder scroll games, fallouts, and so on and so forth.
EDIT: Re-reading this post made me super depressed - I hate nostalgia... Thanks asshole (haha jk!)