For years, Batman got the shaft when it came to his video games. Fortunately for us and the Dark Knight, development company 'Rocksteady' took the helm of this excellent game and really ran with it. They did an amazing job respecting the character and the overall Batman universe. But more importantly, they made a quality game that is very fun to play.
The game looks great, has amazing voice acting (with a special nod to Mark Hamill as the Joker), has an excellent fighting system, and a very good story. That last point is key because most of these superhero games, up to this point, were just mindless beat 'em ups that lacked a good narrative. 'Arkham Asylum' changed all of that & raised the bar for future games in the genre.
Overall, Rocksteady has to be given a lot of credit for revitalizing the super hero game genre. I know most people like the open world of 'Arkham City' better (and I do think that is a slightly better overall game), people shouldn't forget where this award winning series started. Similar to how everyone loves 'The Dark Knight' movie the best of the Nolan trilogy, people tend to underrate 'Batman Begins'. Well, people shouldn't underrate 'Arkham Asylum', as it is an excellent game and definitely worth your money.