Doom 3 was successfully ported to Android, thanks to the same devs that bring the ports of Return to Castle Wolfenstein and Quake 3. Of course the game uses on-screen controls, but if you have Sixaxis it can be used too. According to the devs, the new Doom 3 port for Android is not only supported by high-end devices, it will also run on smartphones like Galaxy Ace 2 or Sony Ericsson Live with Walkman. Sadly, Tegra 2 devices are currently not supported.
Here is a video demo of the game running on Samsung Galaxy Note 2 – it looks really good and smooth.