BATMAN:ARKHAM CITY
The story for Arkham City takes place one year after the events of Arkham Asylum. Quincy Sharp, former warden of Arkham Asylum, has taken credit for stopping the Joker, and used that notoriety to become mayor of Gotham City. As neither Arkham nor Blackgate Prison are in any condition to hold inmates, Sharp buys out a large section of Gotham's slums and arms the perimeter with private military contractors from a group called Tyger in order to create "Arkham City". The prisoners are brought into Arkham City and are given free rein, as long as they do not attempt escape. To oversee the city, Sharp uses psychiatrist Hugo Strange who appears to have his own secret agenda for the city. Batman maintains a vigil over the city, worried that the situation may get out of hand.
The events of the game are set in motion when Two-Face, seeking to gain status among the inmates and other villains outside the city, devises a plan to publicly execute Catwoman. Batman decides for both the safety of Gotham and of his past relationship with Catwoman that he must stop the execution by entering Arkham City himself.
BATMAN: ARKHAM ASYLUM
The Joker attacks Gotham City's Mayor's office but is foiled by Batman, who escorts him to Arkham Asylum. Due to a recent fire at Gotham City's Blackgate Prison, a large number of sane prisoners have been temporarily relocated to Arkham, many of whom are in the Joker's gang. As Batman accompanies the guards taking the Joker inside, the asylum's security is overridden by Harley Quinn, allowing the Joker to escape and take control of the facility. Batman quickly realizes that these events, including the Blackgate fire, have all been part of the Joker's plan and that the Joker had bribed a security guard to help him escape. The Joker threatens to detonate bombs scattered around Gotham City should anyone attempt to enter Arkham, forcing Batman to work alone; however, Batman is able to rely on Commissioner Gordon and other loyal guards after Batman is able to free them. Additionally, Oracle is able to guide him through the Asylum over the radio. Batman is able to gain access to an adjunct of the Batcave he had set up years ago on the island and is able to use his sleuthing skills to learn of the Joker's plan.
These are both must get games, and personally my all time favorites. Arkham Asylum os currently out and Arkham City is set for October 2011.