Bioahock Infinite: Yeah I said it! I can't do justice to Infinite's story line briefly, but I'll just say it's exquisitely well presented, it's actual themes [the game was never at it's core about racism any more then it was about religion, patriotism, classism] about Booker and what his violent nature represents and the effect it has. It's also a narrative that would only work in game form. Part of the reason the twists and turns resonate so much is because we experience them at the same time as Booker, and upon reflecting all of the violent deeds we've committed throughout the game, the bitter truth makes more and more sense. It also has one of the best endings, in any piece of medium I've ever seen. For all of the complexities, it somehow manages to take all of that and make the big important mystery about Booker and Elizabeth surprisingly simple. Anyway, I've had loads of forum chats discussing it's merits or lack thereof so any game that could support that kind of discussion is worthy of mention.
Portal 2: I'm surprised this hadn't been mentioned yet, but this is probably as close to perfect a story as I've seen in a game. The dialogue is consistently funny, the relationships you grow with robots feels more genuine then with a lot of human NPCs in other games, and there are certain moments in the story that lasted with me for days. Wheatley's, er... scene is still one of the more gut-punching moments I've felt in any game, and the ending is appropriately triumphant yet mischievous as well, which sums up Portal in a nutshell.
GTA 4: Niko Bellic is the best protagonist I've ever played as in a game. He's appropriately world weary, but still likeable. He's prone to violence, but fiercely loyal to his family and friends. These traits all make sense given his backstory, and it's such a powerful one that it really drives him as a character throughout the narrative. The other genius with his character is depending on how the player chooses to play Niko [a violent psychopath, or someone just doing mob missions to support his family], it manages to keep the character consistent. The ending is also pretty strong, making the whole 50 hour experience seem kind of pointless since at the end of the day, we're just a guy who's racked up a high body count. There's a reason the achievement for beating the story is sarcastically called: "You Won". The funny thing is, a lot of the critiques of GTA 4 about it not being as fun actually strengthen the narrative in my opinion. The lack of fun makes the violence less cathartic, and more like an errand to run. It normalizes the violence through gameplay to make us understand what Niko feels like committing these horrible acts. It's story was so good that for as impressive as GTA 5 looks, I'm not interested strictly due to the lack of a compelling character like Niko in it
Gone Home: Okay, whether or not this is a game [I'm split on that topic myself], it has a pretty great story, and the way it's told is crucial due to it's interactive nature. I was skeptical that a lot of the praise heaped on it may have just been due to it's portrayal of a marginalized group in society. Basically I was worried it's progressiveness overshadowed any of it's other merits. Fortunately, that's not the case. It's just a really sweet love story, augmented by the time period of the 90 it aptly mimics, and the uncovering of new story bits via exploration makes the discovery of new plot elements feel more dynamic. Yeah, the lack of deep mechanics or skill required to be Gone Home make me less enthusiastic about the stellar story since that was clearly the focus, but hell, it's still a expertly crafted story.
Fire Emblem: Awakening: Okay, this actually isn't fair because I still haven't beaten it yet. What I'll say is that it's a great example of establishing context for why the gameplay matters. It makes me care about these characters, and it sucks to see one of them die in game so much that I have to reset and try again because I don't want to abandon them. Anyway, I can't do justice since I haven't completed it, and for all I know it could end with: "It was all a dream", but for now I'm really digging it.