Sadly the Display of my Galaxy S3 get broken last summer. After some investigation how to get control back I remembered that through the active debug option it should be possible and lucky me, I found someone who wrote this nice tool adbcontrol.jar. You can find this pretty nice tool here.
With that tool it was possible to bind a keyboard with integrated touchpad to the smartphone via bluetooth. Together with MHL to HDMI adapter cable it can be used again without too many limitations.
But to be honest the Bluetooth connection with this cheap keyboard is sometimes a bit sloppy, but it works.
If you have a bluetooth gamepad with can be bound to the smartphone, then you can use it as a kind of game console. But then you have search for proper games which support this kind of gamepad.