Story conveyed through game design - Your Examples?

[Casual Shinji]

Ashley huddling behind you whenever you draw a weapon in Resident Evil 4.

Not only is it beautifully effective in keeping her out of harms way during the action, it re-enforces the roles of both Leon as the protector and Ashley as the protectee. It's one of the most underrated aspects of the game, and of games with escort missions in general.

 

[maninahat]

My favourite example of this is in The Walking Dead Season 1. You get into a fistfight with some hillbilly, and you are doing the usual quick time event stuff to avoid being killed. Eventually, you get on top of the hillbilly and start pummelling him over and over. What happens next is totally organic, in that as you are kicking the guy's ass, you (and the character) either notices you've already won and stop punching, or you get too wrapped up in the excitement and they beat the guy to death. It's a neat way to make the mechanics represent the emotional state of the character.

Also, I should give an honourable mention to Bioshock, because as much as we jibe about it now, I was genuinely impressed by the way in which the game lampshades the way the player obeys the voice in their ear without thinking about it, within the actual story.

Also there is The Stanley Parable, which takes the above to its logical conclusion.

 

[Silvanus]

I think the one that sticks out in my mind is Final Fantasy VII.

Sephiroth was spoken of as a legend early in the game. You first see his work when you find all the blood splattered everywhere in the building--which was a real shock for my younger self because nothing like that had been in the game yet. So I knew this guy meant business.
Then we came across the Midgar Zolom, something that was easily stomping my party into paste, impaled on a tree like it was nothing.

While it's true that those events served to create a huge sense of awe (and foreboding) surrounding Sephiroth, remember those acts weren't actually committed by Sephiroth, but Jenova taking his form.

Of course, we-- and Cloud-- don't know that at the time, so it serves.

OT: Anything by Team ICO, Braid, Limbo, Silent Hill 1 & 2 (and probably 3; haven't played 3).