There were several things that stood out for me in this excellent game, the story, the combat and moving through the world.
The story was very compelling, I wanted to know what was going to happen next, this is something that not many games can achieve in my opinion. Backing this up were the excellent characters employed, obviously The Joker was acted and voiced extremely well, but the supporting characters also played their part.
Combat is mostly melee and differs from many games that had come before it in the way it seemed to flow. Taking on multiple enemies and performing the combo attacks that lead you from one enemy too the next is very enjoyable, and the controls never seem to get in the way of this.
Lastly, how Batman moves through the world really makes you feel like you are playing as the real Batman. The way he can move in all directions of the 3D space is very special.
The only complaint I would make is with Detective Mode, it seems like you needed to be in this mode all the time which did ruin the graphical appeal of the game somewhat. Still, I am definitely getting Batman: Arkham City when it comes out soon.