Shadow of the Colossus used both immersion with the boss fights and the lack of when you're on the fields travelling to properly build the game up, an experience I haven't seen elsewhere.
Let me explain: When you're travelling to the colossi, you are given time to reflect on your character and his actions. In otherwords, you compile the information from your actions, what you've seen, and just plain speculation to define this Wanderer, telling his story in a cutscene you control. When you're travelling, the Wanderer is a character you are examining.
However, during the boss battles, the intensity of the fights, the grip slowly fading, and the magnitude of the colossi brings you straight back into the game. You are now concerned with beating this things, sometimes to stay alive, other times because you are now trapped with them, and still other times for completely different reasons. Even when you know HOW to beat them, they still register as a real threat and your mind switches your thoughts to deal with these things at the exclusion of other concerns. In other words, when you're fighting, YOU are the Wanderer, meaning that the next time you travel, it's your actions you're examining projected onto the character.
So it uses immersion to add to the action, and the lack of it for the story, which in turn makes every story different to everyone.