Grand Theft Auto
Grand Theft Auto 4 is apparently the biggest and best game to ever be released, and the gaming press thinks it has an Oscar-worthy story (although with shit like Juno receiving so much praise, it could be said that GTA4's tale is better than Oscar-worthy). To me, the story told in GTA4 is not the one of Niko Bellic's rise thorugh the ranks of the criminal underworld and getting revenge on an evil bastard. The story of GTA4 goes more like this:
Niko Bellic picks up his girlfriend, Alex, from her middle East side apartment. She tells him that she got a bikini wax just for him, and that he should be honored to be written about in her blog. They go to Club Liberty and get wasted. Attempting to drive home drunk, Niko crashes into a cop car, sending them into a high speed chase over the bridge to Bohan. Niko crashes the poorly handling van a few more times, causing it to explode, killing them both.
To me, that is the story told in GTA4, and it is far more entertaining than any tale of revenge or rags-to-riches. This perfectly embodies a storytelling ability that only video games have over other mediums...specifically the sandbox genre. The storyline of Oblivion, for me, is not about how a noble warrior saved the world from a spreading evil, but about how a solitary ranger ascended a massive snowy mountain just to see if he could.