Go buy this game right now.
I bought a PS3 pretty much just so I could own this game. It's filthy how good it is. The obvious appeal is the massive size of the city, and how much there is to do in it. It has a GTA-type feel to it, except you're fucking Batman, and instead of driving cars, you're jumping from roof to roof, swinging with your bat-claw, and gliding with the cape.
The part of the game that really gives me a boner is when you find a room with a dozen armed thugs, and you swing up to a gargoyle, hide from them, and pick them off one by one. You can hear them talking to each other, getting scared, and I swear to God you just feel like you really are Batman. I found myself, sitting alone in my living room, saying "Criminals are a cowardly and superstitious lot" and I wasn't being ironic, I was just totally caught up in it.
The story is pretty solid: below par for a comic but way above par for a video game. The voice acting is really good, I think they got the guy who has done Joker's voice for the cartoons for the past twenty years, which is pretty sweet. The fight system is fun, most of the time you fight three or four guys at a time but every once in a while it throws twenty thugs at you all at once, and it still works. The boss battles are decent but visually incredible. The Solomon Grundy fight was amazing.
The main story has a lot to do but it seems like there will be hundreds of hours of side quests. Any chance I had of going and getting a social life are pretty much shot.
Seriously, go buy this now.