My two:
Very cliché, I played Ocarina of Time a ton as a child, have memories of playing it both on N64 as a wee child and on game cube as a less small child. Never got past water temple even with the game guide.
Yu-Gi-Oh forbidden memories. Played the crap out of that game on play station, constantly playing on free play praying for the cards I would need to get further. I was never able to beat more than 1-2 of the high mages. Watching speed runs on the game it turns out I was never ever going to beat that game as a kid. The final 6 are just disgustingly brutal.
GTA 3 / Vice City. My brother had a PS2 and would let me play. I never bothered with the story / campaign, I just liked to wonder around, steal cars, and drive. I enjoyed using cheat codes to spawn tanks and get full wanted level and outrun the cops.