While many don't consider the Kindle Fire a true Android tablet because it runs a heavily skinned version of the OS, it nevertheless marks the first time HBO Go is available for an Android tablet (it's been available for Android smartphones). Amazon says the app gives you access to more than 1,400 titles, including every episode of every season of the best HBO shows.
You do need a Wi-Fi connection to stream shows and, as noted, you have to be an HBO customer who subscribes through a participating television provider. Most, but not all, HBO customers will be able to use HBO Go on their Kindle Fires. At launch, anyway, the notable exceptions appear to be customers of Time Warner and Brighthouse Communications (both companies' customers can sign into the iOS version of the app on the iPad).
I downloaded the app to the Kindle Fire and found the experience to be similar to using the iPad app. Of course, the better Internet connection you have, the smoother your video will be.