As a fan of Batman in general, I really enjoyed this game. It captures the essence of the Grant Morrison graphic novel of the same name (though it is by no means meant to follow it directly), and you can really get the sense of Batman struggling to maintain his sanity as he faces the inmates of the Asylum. This is the grim and gritty version of Batman, and is much darker than the Batman people are familiar with from the movies.
It does start out a little slow, but very soon, you'll be fighting swarms of bad guys with many useful gadgets, and having boss battles with classic Bat-villains (Bane, Poison Ivy, Killer Croc, and Scarecrow, among others). The Joker is wonderfully insane (and quite creepy), and provides a pretty bizarre commentary of the situation throughout the game. Some of the fights can be a little repetitive at times, but there's enough variation in them to keep them interesting (bad guys with different weapons, using objects in the scene to aid you, stealth attacks from above them, etc.).
The one main issue I have with this product is not from the game itself – it's the use of Games for Windows LIVE. It causes more problems than any other platform I've used, and can make it difficult to even start the game. It has to be installed, signed in, allowed to download updates and check your profile before you begin. You can play through without it, but you won't be able to save your progress if you do so there's not much point.
Overall: brilliant game on an unfortunately bad platform. I highly recommend this game to anyone who likes Batman.