Most android devices can be used as a desktop, when connected to a display through OTG, and connected to Bluetooth keyboard & mouse. Now we have Android devices specifically made for using external displays - the Android Desktops.
Remix IO and Remix IO+ are upgraded versions of the Remix Mini.
iConsole.TV started out with the dream of building an Intel core i7 desktop computer with Android, in direct partnership with Intel. Unfortunately Intel stopped supporting them midway.
Ouya is the famous pioneer Android game console that inspired other Android game consoles, and Android boxes in general.