Only controllers. On certain games I cannot play them any other way. There was a game that wouldnt let me invert and I hucked the game across the room, was a long time ago but I would probably do it again.
I don't when running, but I do when flying (since that's natural in flight) - and that is only with controllers. No option for controllers sometimes, so didn't say anything.
I always invert for FPS/MMOG/anything with first person type view. I never invert for PS2 games.
"There is at least as much need to curb the cruel greed and arrogance of part of the world of capital, to curb the cruel greed and violence of part of the world of labor, as to check a cruel and unhealthy militarism in international relationships." -Theodore Roosevelt