There is a "Road to Arkham" comic which serves as a prequel to Arkham Asylum. It was written by Paul Dini with art by Carlos D'anda (who is responsible for the awesome character bio artwork in Arkham Asylum) It was released as a pre-order bonus for Amazon customers who purchased the game, and as a digital release available exclusively for Sony's Playstation Portable console.
There was a 5 issue miniseries connecting AA to AC titled "Batman: Arkham City," again, written by Paul Dini and featuring artwork by Carlos D'anda. In addition to that, there was a 7 issue digital only book. However, the trade paperback edition of the miniseries collected both the miniseries and the digital series in print.
Following that, there was the Batman: Arkham Unhinged digital first series. It is currently on its 58th chapter and is still going; most likely until the Arkham Origins tie-in series is released. This series has been collected in print form and is currently on its 15th issue.
There was also a 6 chapter digital comic which, I believe was something of an epilogue to Arkham City titled Batman: Arkham City: End Game. I believe it was collected as a one-shot print edition.
As I said earlier, there is also an Arkham Origins series on the way.
Here's the full list (along with links to purchase the books):
Batman: Road to Arkham (your best bet is eBay or Amazon, unless you have a PSP or Vita)
Batman: Arkham City ($3.99 per issue; 5 issues; also available digitally via
Comixology)
Batman: Arkham City ($.99 per chapter; 7 chapters; digital exclusive available via
Comixology)
Batman: Arkham City Hardcover ($22.99; collects 5 issue miniseries and 7 chapter digital series in a single Hardcover volume; available at
Warner Bros. Online Shop)
Batman: Arkham City ($16.99; collects 5 issue miniseries and 7 chapter digital series in a single trade paperback volume; available at
Amazon)
Batman: Arkham Unhinged ($.99 per chapter; 58 chapters and counting; available via
Comixology)
Batman: Arkham Unhinged (print edition) ($3.99 per issue; 15 issues and counting; available wherever comics are sold)
Batman: Arkham Unhinged Volume 1 Hardcover ($22.99; collects issues #1-5 of the print editions; available at
Amazon)
Batman: Arkham Unhinged Volume 1 Trade Paperback ($14.99; collects issues #1-5 of the print editions; available to pre-order at
Amazon)
Batman: Arkham Unhinged Volume 2 Hardcover ($22.99; collects issues #6-10 of the print editions; available to pre-order at
Amazon)
Batman: Arkham City: End Game ($.99 per chapter; 6 chapters; available via
Comixology)
Batman: Arkham City: End Game One-Shot ($6.99; collects all 6 chapters of the digital series in print; available wherever comics are sold)
Damn, that was time consuming.