BioShock is a story like no other, for one thing, it takes place underwater. You play as a man whose face you arguably only see once as an adult, only in a picture, and right in the intro. Other than that, you see a few pictures of Jack (the man you play, no last name given, though one could assume it's Ryan.)
Jack is on a plane that crashes, and when he swims out of the fiery wreckage, he finds a submarine that takes him to Rapture, an underwater civilization that was created for the better-than-average people, to breed super humans. Literally. Andrew Ryan created Rapture, as well as materials humans could inject into themselves with syringes to make themselves even better than they were, to the point of literally having super powers (EX; telekinesis, electricity control, fire creation, and even mind control.) These superhumans are called Splicers. Jack comes across a syringe and naturally injects himself. His DNA gets altered, he stumbles and falls off of a balcony. He blacks out, and comes to a few times. The first time, he sees one of these splicers, inspecting him. The second, he sees a Little Sister and a Big Daddy.
The Big Daddy, protects the Little Sister as she collects Adam out of the bodies of the dead Splicers. Throughout your journey, you will come across several Big Daddies and Little Sisters per level (about 3.) You will have to kill the Big Daddies, which is usually easier said than done, and either Harvest or Save the Little Sisters. If you Harvest, you get more Adam. If you save, you get rewarded with Adam every third Little Sister, which equals to the same amount of Adam, and the woman who takes care of the girls is much more pleased with you (on Xbox 360, there is also an achievement for saving every little sister, and not killing any!) There are three different endings to this game, the good, which is when you've saved the Little Sisters (though you can Harvest only ONE and still get this ending,) bad, which is if you've Harvested even two of the Little Sisters, and neutral, which is hard to get, and not very impressively different from the others. On the other hand, if you do the playthrough three times, you definitely will get all of the achievements (for Xbox 360) and trophies (for PS3.)
The game, is incredible, probably the best I've played in recent years. Other than that, the game doesn't have a lot of replay value, so if you're going to replay it all three times, you should probably space it out pretty far apart. The game is definitely worth playing, but you should definitely save early and save often. It's been glitchy for me, especially at the end. Trust me, the last thing you want to do if you're trying to push through the game, is replay the last two chapters.
Definitely worth renting, but I don't feel like I wasted my money by buying it, either.
Have fun, play hard.