It is necessary to test the game on as many different devices as possible. The game might look and feel very different on tablets and phones and even on two similar phones. Moreover, some phones define their own ways of handling the application life cycle, especially pausing and resuming. Testing on a few major brands and popular devices is always recommended.
Testing on different devices is not always an option for many reasons. In that case, we should test at least a few different resolutions in an emulator. An emulator can never substitute testing on a real device. It is missing many features of phones and tablets and, of course, even the implemented functionality is just an emulation.
To run the game on an emulator, first start the Android Virtual Device Manager from Eclipse. The option is located in the main button bar and in the Window menu.