Bioshock

Throughout the game, you have little sense of who your main character is. All you know is that his name is Jack, and he's crashed in the middle of the Atlantic ocean, somehow surviving the terrible plane crash. He's the only one alive, and he finds a lighthouse. A few (extremely horrifying) moments later, you're in the underwater utopia of Rapture, one of the most iconic places in all of gaming history. There's reason for such a statement as this. Rapture is beautiful in every sense of the word. Or was. It's now a decaying Eden, filled with addicted men and woman with super genetic powers, and little girls who steal peoples "ADAM" followed by hulking and nearly indestructible Big Daddies. Sound disturbing? Indeed it is.
As you progress through the game, you earn loads of different abilities and weapons, giving you limitless options of how you want to annihilate your foes. This is what sets Bioshock apart from other first-person shooters aside from its incredible story. It lets you play any way you want, giving you full control over any situation without making the game any less difficult. It also strays from Metroid style gameplay by letting you choose what plasmid or weapon you want, when you want it. Bioshock's combat stands tall above others in its genre.

Though Andrew Ryan takes most of the story credit in Bioshock, one of the most interesting encounters I've had in any video game is with the savant Sander Cohen. He loves his art. And no matter what form it's in, he still loves it. You go around this level taking pictures for the madman, and hanging them on a portrait made up of frozen splicers. It's haunting, and I still think about some of it's moments to this day. Sander Cohen is like Arkham Asylum's Scarecrow, he's not the main event, but he's one heck of an opener.
Another thing that sets Bioshock above and beyond most stories (notice how I didn't say games) is it's sense of atmosphere. A deep, tense, dark, horrifying, twisted atmosphere. The underwater once-utopia is stunning to look at, and it's six years old now! Each character is uniquely dressed, but really it's hard to notice when you're too busy not dying. Rapture is a dark, glorious masterpiece, and remains as one of the best story universes ever.
Bioshock redefined the first person shooter, and the world has been better off for it. If you haven't played it, do so immediately. It deserves this spot on my list.