There have been many superhero games throughout the years. Most of them have been sidescrolling "beat 'em ups" in the vein of the Final Fight series. Others were horrible adaptations like the Superman game for the N64. Arkham Asylum has been, with few minor exceptions, one of the most on-point adaptations of a superhero property into a game that I have ever played.
First, the format, a 3-D "metroidvania/Legend of Zelda" type deal where new tools open new areas and items to get, plays nicely into the feel of the game. That same format also helps with the "lone hero" feeling that is in many ways the essence of Batman. You feel like yes, you are alone, but you aren't out of your depth. Also, the classic animated series voices help set the tone of the game; dark with just a bit of humor here and there.
The game world is lush and well rendered, created in that gritty style also befiting a game about The Bat. Ruined sewers, secret tunnels, and crawling through airways and up walls all give this sense of being secretive, careful, and thought out. The world you have been given to play in is tailor made to adhere to the common action/stealth tropes that exist in other Batman works.
The combat and movement can be . . . halting at times. In particular the "hold button to run" command, something that I thought I had seen the end of when analog sticks came to prominent use, feels forced and unintuitive. When the combat flows, slighlty pauses on a big hit, and Batman is leaping to and fro kicking, punching and generally kicking ♥♥♥, it looks good, and it feels good to be doing it, but there aren't any ways to "do" the one move you like, really. And the combat system is at its best when you have maxed out all your available attack options.
The fightable enemies are simple and never waver from the basic human stock of "Joker goon fight"; they are either unarmed, armed with a melee weapon, armed with a firearm, a stun baton, or they are giant mutant freaks. This includes the "boss fights", making the gameplay and world far more engaging than the actual combat. That said, most of the combat is short and simple. I think the longest normal skirmish took maybe a minute. And the best parts of combat aren't specifically the combat so much as the setpieces where you have high perches to disappear to. You can swoop down, take out a goon, and then grapple up into the shadows, listening and watching as the other goons start to freak out as you take them down one by one.
And finally the story, which at least matches the quality of the old animated Batman series movies for plots. Joker has a crazy plan, and Batman has to stop him. The winding way Bruce has to do this is what makes up the bulk of the game. Some of the story points feel contrived, but overall, the story flows from point to point in a logical way. What helps in this is that Batman himself often tells the player (and Oracle over his headset) the next step. And when Batman tells you something in this game, a combination of the voicework and the writing just seems to make the next plotpoint make sense.
With solid voicework, a lonely, beautifully crafted world, and a combat and stealth system that is only sometimes marred by its own trappings, this is a solid, wonderfully made title that anyone who counts themselves as a superhero fan in general or a Batman fan in particular should own.