Thomas Was Alone is a very good example of a game that is able to keep your attention with narration. It's especially amazing to me that the narration bring alive "characters" that are nothing more than different shaped blocks. You almost get the sense that it's all in your head, that they really are nothing more than blocks, yet you still develop feelings toward them. It's a really clever way of adding story where none is actually visible.
Some RPGs use a narrative method of story-telling, as well. In Final Fantasy Tactics, you're playing a slice of history that actually differs from the "truth". It reminds me of "The Real Story", a very interesting science fiction novel that tells you what officially happened, then presents you with what REALLY happened.
