You're probably not quite ready to trade in your copies of Catcher in the Rye and Sense and Sensibility for a GameFly subscription but that doesn't mean that it isn't completely impossible that you may someday use one of the following story rich games as a teaching tool in your own classroom.
Keep an open mind while you take a look at these trailers and articles:
Coming Soon! Elegy for the Dead, admittedly a very creepy name, but it has a unique and much less threatening premiss. In this dystopian world you'll explore a wild landscape while simultaneously writing the game's storyline. It's been described as a sort of interactive mad libs.
If you can get beyond the fighting parts, Assassins Creed features some of the most gorgeous architecture and intricately detailed historical accuracy of pretty much any game I'm aware of. In this series you can visit and explore life during the third crusades, the renaissance period in Italy, the American Revolution, and the fourth installment is rumored to take place during the French Revolution. I've actually found myself completely engrossed with the scenery and plot-lines of this game simply watching others play. It's very cinematic.
Take a look at this conversation between two characters in the game:
The Novelist is another newer game that may have some interesting potential for classroom use, especially in regards to human psychology, motivation, the idea of free-will etc... Essentially you make choices for each of the family members and "write" their story via the outcomes of their actions and decisions. It rates pretty high on the strange-o-meter but I still think it could have a degree of educational value.