The simplest and easiest thing to say would be that Viber works on iPhone, iPad, iPod Touch and Android devices, with some exceptions.
Here is a list of currently not supported devices or systems by Viber.
Android OS less than 2.3.6
They are not supported but a friend of mine has a Samsung Galaxy Tab with WI-FI only and Viber works just fine on this device. I’m sure that in the near future we will have a list of tablet devices on which Viber works OK.
HTC Wildfire, HTC Hero
For some time, Viber was unavailable for download from Market for those two devices. Now they are available, but still known as problematic.
Note on Jailbroken iPhone, iPad or iPod Touch
They are supported, but the Jailbreak interferes with Push Notifications mechanism and this causes problems in terms of Viber’s functionality.