During the Credits
During the credits of Arkham City there is some extra audio dialog from one the villains, check out more details and spoilers below.
The extra audio contains Batman checking his voicemail to find that the Joker has left him a message singing the song “Only You.”
After the Credits
After the credits there is a message explaining that a New Game Plus has been unlocked with previous items already unlocked, harder enemies, no counter icons, and alternate Batman outfits.