Ico (PS2, PS3)
I even remember writing about this on my blog. I'll paste some text from the previous post:
Ico starts off slowly, with a long cutscene. You get thrown into a murky world and have to work out the controls. The world's not actually murky, but playing it on my HD TV certainly made it look so. I worked my way through the castle, until I found the girl in white. I knocked the cage down the tower, and rescued her from the shadow monsters. I then couldn't find a way out of the room. Huh.
Never mind, I thought, I'll come back to that later. I'd been playing for 40 minutes or so. I turned the console off, and then thought ... hmm, I wonder if the game does save at checkpoints?
I have only ever played this for five minutes, and it made my head hurt.