Absolutely fantastic game. I bought it yesterday, and I haven't been more excited for a game than GTA IV I think. Definitely the best game I've bought all year.
I honestly can't fault anything. The visuals are stunning, the story is great so far, the combat is just WOW...
I've never really been a fan of superhero games as most are too childish, but this game feels very grown up, and has a gritty/dark feel to it. Even if you're not a huge Batman fan, but love fast paced hand to hand combat you should love Arkham Asylum.