Batman: Arkham Asylum is one of the best superhero games of all time -- certainly the finest of this generation.
Despite that, however, Batman: Arkham Asylum is a tremendously entertaining game and well worth playing even for those who don't know who Frank Miller is (The Dark Knight Returns is, to date, the only Batman comic I've read). Its influences are clear: its atmosphere and level structure are reminiscent of Bioshock, while its action is akin to most modern action games. The missions are varied and interesting, as are the boss battles that crop up throughout the narrative.
Considering how muddled the stories of some superhero movies or superhero games can be, Arkham Asylum stands out as an admirable example of a finely crafted narrative. You always know why you are where you are, and why you're doing what you're doing -- which is more than one can say about a few of this generation's biggest games, such as Gears of War.
The game has no multiplayer component, but it comes with a set of challenges and beat-em-up stages that can keep you occupied well after you complete the campaign, which will last you 10-12 hours.
I highly recommend picking up this game -- it's one of 2009's best.