A car drives on the wall.
How to use FEZ to do that?
In Taiwan, someone sells the similar car with infrared remote control.
The price of this car is NT 999 (USD $34), not very expensive.
http://shopping.pchome.com.tw/?mod=item&func=exhibit&IT_NO=DEAS0J-A42278230&c=A05
I will buy one to try and maybe I can use FEZ+ infrared remote controller to control the car.
I don’t think there will be any problems with using a FEZ for this. It might be an overkill to use a FEZ as you probably could use just a PICAXE and a H-bridge.
Good luck and keep us posted 
How does it stick to walls?!
I am not sure, but I think maybe use a vacuum.
Should be no problem to control it with fez. It uses two sets of wheels (left and right) so a h-bridge or the fez dc motor driver shield should work fine.
Shield:
http://www.tinyclr.com/hardware/1/fez-domino/#/grid/item/118/
I guess you might really need a board with just the chip and motor controller. That thing really needs to be very lite.