It would be a great game anyway, but as a Batman game, this can be considered a gaming classic.
"This island is under my control, that's right boys and girls, mine,mine,mine,mine, the plans I have for this place, it's going to be glorious!"
The premise of the game at its core is simple: when Batman brings The Joker back to Arkham Asylum (for the criminally insane) after his latest escape, Joker breaks free from the guards and prevents Batman from following him, revealing that the prior escape and subsequent capture were merely part of a plan to take over the asylum. Thus begins a very long night for the Dark Knight, as it isn't just Joker, but several members of Batman's rogues gallery that are on the island as well, free to cause chaos or just revel in the chance to try and kill Batman again.
Some of these villains include Bane, who you should lose to at least once to see how he finishes Batman off (if you've read or followed the comics, you know what to expect), and Scarecrow, who even people unfamiliar with the Batman mythos should know about due to his appearances in Batman Begins and The Dark Knight. The times that Scarecrow gets involved are among the most memorable in the game, calling to mind the insanity effects of Eternal Darkness but not feeling out of place.
Another villain of note is The Riddler. Though he does not physically appear in the game, he will occasionally taunt you via the communicator (which generally is used for communications between Batman and Oracle, aka Barbara Gordon, who keeps you appraised of the situation in Gotham and important issues on the island) and provides you 240 challenges to complete. Though optional, these will unlock many extra features in the game and are worth one's time to undertake. Completing a challenge will also net you experience points (which can be used to upgrade Batman's tools, armor, weapons, and skills).
"C'mon boys, he's just one man! ...One man dressed like a lunatic and armed to the teeth, [laugh] GO GET HIM!"
One of the first things that comes to mind when one talks about Batman is his utility belt, and this game does not disappoint. Though you start with an infinite supply of Batarangs and a grapple gun to get to high places, more tools will be added as you progress through the game. You'll get the tools at certain plot points, and in Metroid-style can go back to earlier places in the game to deal with obstacles that you could not earlier. On top of all of this is Detective Mode, an alternate viewing mode that serves as a mixture between an x-ray device and the scan visor from the Metroid Prime games that lets you see things like hidden walls, fingerprints, certain Riddler challenges that are otherwise invisible, and the condition of the enemies you are facing.
When not exploring Arkham Asylum (which spans an entire island and several buildings), you'll find yourself in one of two situations to take out the enemies. The first one is combat, which can involve over 20 baddies in some situations. Early in the game your moves are limited. Square does a context-based attack, triangle is a counterattack (with the exception of Hard mode, an indicator will appear to let you know that an enemy is about to attack: blue means it can be countered while red means it cannot), circle makes Batman attack with his cape to stun anyone in range, while cross can be held to run or double-tapped to evade. Along with this is a ground takedown against downed enemies, which leaves you open to attack but also guarantees that the person you hit will not bother you again. Though one can get by with button mashing early on, the game does a good job of mixing things up later by introducing enemies that need to be stunned or evaded before they can be hit, while others must be hit with the Batarang (a quick-tap of L1 will make Batman throw one at a random enemy) to trip or stun them first. Successful attacks will increase the combo meter, and you will want to get this as high as possible in every combat situation. Trophies aside, building a high combo will allow you to use moves such as the throw and instant takedown as well as give you experience points. Other bonuses, such as not getting hit and varying the moves in a single combo, will net you more XP.
"Note to self: need to order more henchmen. Good ones this time..."
The other situation is known as predator, and this usually happens when Batman finds himself in an area where the thugs have guns and are more spread out, though not always. Here a stealth approach is encouraged, since bullets do not bounce off Batman like a certain other DC Comics hero. The game usually gives you different ways to approach these: do you hang from the ledge and pull the goon off as he walks by, or do you hang from the ceiling gargoyle and swoop down on the unsuspecting fool and make him hang upside-down? Later in the game, you may find it prudent to place some explosive gel on a weak wall and blow up said wall to knock the ugly out under the rubble, but you may never find it old to glide from up high to kick the guy down and slam his head into the ground.
Predator situations are among the more entertaining in the game, as the music (all of which is original to the game, so don't expect the classic Danny Elfman theme or any Zimmer/Newton-Howard music to show up) will add instruments and become more grandiose as you take everyone down, along with the anonymous henchmen getting more and more scared as you go. Instead of just breaking patrol, spreading out, and looking for Batman, the boss's lapdogs will start to panic and just randomly shoot while yelling at whatever may or may not be there. While many games create fear for the player by putting you in situations where you never know what's around the corner, this game reverses that by making you, Batman, the one instilling fear in your foes.
"He may look like an idiot and talk like an idiot, but don't let that fool you! He really is an idiot!"
A large part of the atmosphere in this game is provided by the voice acting. Three actors from Batman: The Animated Series and its sequels and spinoffs reprise their roles here: Kevin Conroy as Batman, Arleen Sorkin as Harley Quinn, and Mark Hamill as The Joker. The acting for the rest of the characters is superb, but these three stand out, as they have been playing these roles since 1992 and get the chance to show that they know these characters inside and out. From Batman's occasional inner monologues to Joker's PA announcements, there is no shortage of entertainment to be had, even if it sometimes comes from just standing still and listening to Joker make a Three Stooges reference. Of note is that Joker will also chat it up during the predator sequences; at first he will be threatening to Batman and inspire/scare the goons with confidence, but as you take them out, he may start taunting the lone gunman instead for his own amusement.
"I'm not coming in without a fight, Arkham!"
Aside from the main game, there is also the Challenge Mode, which consist of various combat and predator challenges that let you shoot for a high score or try to finish as quickly as possible. These are unlocked, like everything else in the game, by completing Riddler challenges. Also, with a PSN connection you can download challenge maps where The Joker is playable, and you will learn rather quickly that trying to play him the same way you would play as Batman won't help much. Though you can't play him in the main game, these make for a nice addition that you don't have to pay for. The extra Blu-Ray space was put to good use as well; if you put the game in but go to the video tab, you will find a series of behind-the-scenes videos that shed some light on the design choices and how the game came together; for example, the main reason they chose Arkham Asylum as the setting is that it's a place where many of the villains that Batman faces would reasonably be at without having to come up with a contrived reason.
"Paging Dr. Bat, paging Dr. Bat. Is there a Dr. Bat in the room?"
Though the game is not perfect, particularly with the pacing later in the game and some of the boss fights being somewhat underwhelming, it is not enough to detract this game from being recommended. Even if your favorite member of Batman's rogues gallery isn't active in the story, there will at least be something in the game that hints that he or she has been to Arkham before, such as election merchandise for Harvey Dent (Two Face) or Jack Ryder's news radio broadcast. This immersion into the Batman character, the mythos, the great gameplay, and high replay value (difficulty modes, the Riddler challenges, challenge mode, and the desire to hear Joker say his stuff again and again) make this game worth every dollar, pound, euro, krone, or whatever currency you spend.