This is easily one of the most fun, cinematic, epic, well-made video games in a long time. This would easily make my list of top ten games in the last century as the experience is amazing.
The atmosphere in the game is the highest point of this game (if there could be only one). Taking place in 1960, the game has a great old feel to it with radios playing in bars and even the enemies using slang of the day. BioShock has created the best atmosphere in a game ever created. Fuckin' period. You'll feel like you're there, in the underwater looney bin of a city known as Rapture.
The gameplay is simplistic at it's core: complete goals, find powerups, manage said powerups (you must purchase slots for different power ups and plasmids), and shoot things. However, these powerups if not found, can only be purchased with Adam. As Kaz said in the first post, Adam is a slug, a parasite infecting little girls whom are called Little Sisters which give off a potent genetic material that all the citizens of Rapture crave. Harvesting Adam is accomplished by catching a Little Sister. Catching a little kid . . . not too hard right?
Little Sisters are guarded by Bouncers, better known as Big Daddys and Rosies. They're lumbering giants with potent weapons, heavy armor, and only one goal in their lives: to protect Little Sisters. The game gives you an interesting moral choice when it comes to harvest a Sister however, because Harvesting (the G-rated word for "killing" in this instance) gets you more Adam, players may be less inclined to save the little girls (which is the other choice).
The soundtrack is another incredible feat. I won't say anything, I'll let you listen for yourself. 2K was nice enough to allow free downloads of the score!
Bioshock is worth playing just for the lovely level design and seriously clever and entertaining story. The game also has a great cast of insane and/or fascinating characters, though you mostly become familiar with them only through voice recordings. Dr. Steinman--the twisted wannabe Picasso of cosmetic surgery--is a particular favorite of mine. I found the last 1/3 of the game a bit dull compared to the rest of it, but only because it seems to let the cat out of the bag just a bit too early. There was simply nothing the game could do to top itself after... Or, actually, I can't say without spoiling the game.
As something of an asides, a friend of mine was asked if he was saving or harvesting little sisters, and he said shocked "I'm not a monster!". You have to admire a video game that can make you feel like a choice has real moral implications. Most people actually do what seems like the right thing in it just so they don't feel like dirt. I know I did. Great stuff.
I read a glowing review in EGM yesterday about the game. However it has no multiplayer...and when I buy games the first thing I look at is replay ability. Multiplayer is a factor but if the campaign is so fun to go through on the 2 or 3 or even 7th time around I would get the game.
Example I completed halo One's campaign about 15-20 times. Halo two's I completed about 8 or so times. Even games like star wars battlefronts which I only played like a few levels into the campaign it still had a fantastic multiplayer.