I may throw this phrase around too casually, but the story in this game blew my mind. It was insane. In order to wipe away a debt, Booker DeWitt is going into the floating utopian city of Columbia to rescue a girl imprisoned by the ruler of that city. I don't want to spoil anything, so I'll just say: be warned, the plot definitely requires you to do a good bit of thinking before you understand it, but once you do, you'll see the epic brilliance of the story. I honestly think the writers of this game should try their hands at sci fi movies.
As for the gameplay. It's a fairly basic shooter with mechanics that kind of reminded me of a less explosive version of Borderlands. You uncover a number of abilities as you progress through the campaign that give you an edge against some of the more difficult enemies. You are equipped with a claw/razor blade thing that allows you to utilize the skyline rail system and make for some pretty exciting, fast-paced combat sequences. The difficulty is perfect. Nothing is impossible, but it's not a complete cakewalk either.
Visually Bioshock: Infinite is beautiful. The city of Columbia is incredible and makes for some trippy scenery. The general layout and details of the floating city are what really drive this game home if not already for the story. Sidenote: the voice actors are pretty awesome too.
I'd say my only qualm with the game was how brief it was. I did a lot of goofing off and poking around throughout the campaign and it still only took like 25-30 hours. I would have expected more for a game that has no multiplayer and is designed purely for its campaign. Once I completed the campaign there wasn't much to do. That's why it's probably best that I did not buy it initially. I waited for the game to go down in price, so that shouldn't be a huge issue. I'm also given to understand there's a good bit of DLC for the game as well.
Considering the brilliance behind the story as well as the setting and in light of the significant price drops I think Bioshock: Infinite is definitely worthy of adding to your game collection. Check it out.