If you have the move controller with the camera, then you can get some shooting games like House of the Dead, RE: Chronicals, and the shoot. As well as the Move sports games. You only need one hand for that.
Even Heavy Rain might work if you have the edition that is Move compatible.
Well if you have a Wii You can probibly play any game that only uses the wiimote and not the nunchuck or other accessorry. It would also need that Wiimote not to be used sideways. Animal Crossing City Folk can be played with just the wiimote and only your right hand. Not probibly what you want to play but there are probibly other games like that. Anyone know what they are? Keep in mind that if the wiimote needs to be sideways so that the d-pad is being used by the left hand it doesn't count.