What can I say that hasn't been already said about Batman: Arkham Asylum?
The gameplay is top-notch. I enjoy the whole "Predator-style" feel to it. Sometimes you can go in and beat a whole group of thugs without breaking a sweat. Sometimes you have to be smart and use stealth to advance (because in certain scenarios, it is a requirement). In other words, Freeflow combat is great, the stealth elements work nicely, and it's fun to have Batman's gadgets at your disposal. You defiantly have the feeling that you are Batman himself (which sounds stupid, since you are playing as Batman, but I hope you understand what I mean).
Environments are fantastic. It has a nice, dark atmosphere to it. Whether it is in the sewers, the botanical gardens, or Scarecrow's nightmare sequences, it's dark, it's gritty, and it's great.
The story and acting are just as good. Kevin Conroy and Mark Hamill were excellent in their respective roles as Batman and The Joker. Sorta makes me want to pick up Batman: The Animated Series on DVD.
My only (and minor) complaint about the game is that you might end up leaving the Detective Mode vision on for a majority of the game. Sure, it is very useful, and you can detect an enemy's position in whatever room you are in, but that is where the problem is. You obviously don't want to walk in a room where the inmates have weapons and you don't know about it. So you have to have it on for a long while. But that was how I played the game, so it might be different to other players on how they played it.
It also sucks that the 360 version doesn't have The Joker challenge maps. It makes you wonder what went into the decision to make those challenge maps a PS3 exclusive. There is a point in the game where you do control The Joker for a little while, but because you are not beating up officers, you just wish that maybe in the near future that Eidos is nice enough to offer those challenge maps for a low price on Xbox Live.
Still, Batman: Arkham Asylum is one of those games that everybody needs to play. Whether you are a Batman fan or not, this game is a must buy.