I might look odd for this, but Fallout: New Vegas is probably my ultimate favourite game.
New Vegas is anything but a flawless game- in fact, the first time I tried to play it, I absolutely hated the game. But over the course of a year or so, Obsidian really went out of their way to patch it up as much as they possibly could (since they were given only eighteen months to develop it by Bethesda, rather short for a game this scale) and turned it into something jaw-dropping.
To begin with, the dialogue and characters in this game are simply fantastic, and some of the best you'll ever come across in gaming. They will connect with you in really special ways and even change your course of action throughout the story. For instance, I met a follower named Veronica- a Brotherhood of Steel member- who, over the course of a week of travelling with me, became someone I genuinely cared about. When my employer in the game's main quest, Mr. House, demanded that I eliminate all existence of BoS in the Mojave Wasteland, I realized that Veronica would loathe me forever and I would never see her again. Thus, I proceeded to murder Mr. House- just beforehand, I explained to him that he had betrayed my personal interests- and then left his home, told Veronica that we should leave, and went on with my journeys through the wastes.
The fact that a collection of pixels combined with a voice could lead me to have emotional conflicts with what I should do next is something that no game with forced 'moral choices' has ever placed upon me. This is only one example of many throughout the game, however. There are plenty of other situations just like this, and the characters and dialogue throughout New Vegas are just consistently works of art.
New Vegas also provides excellent exploration and combat, all very well-balanced and fun. The game makes you feel powerful at what you do, but being a true RPG from a true RPG developer, also ensures that you have plenty of weaknesses and faults in your character. The possible character builds are nearly limitless, and there are narrative and gameplay choices abound. I was amazed by how dialogue with almost every character lands you in another interesting quest, and you'll find yourself with tons of distractions no matter where you go.
This game simply changed my perspective of gaming in a way that I can't quite explain, but its atmosphere, masses of content, excellent humour, addicting combat, wonderful design, and even touches of realism really blew me away.
Runner-ups: Oblivion, Destroy All Humans! 2, BioShock, Assassin's Creed II, Far Cry 3, Star Wars Battlefront II, Sly 2: Band of Thieves, Red Dead Redemption, Shadow of the Colossus, and Batman Arkham City.