I was thinking about this last night and came to the conclusion that it would be very difficult for a major fire.
Most likly thing to happen would be the PSU/GFX/CPU goes pop then the computer turns off.
If it does turn into a fire then its sealed inside the metal case and there isnt exactly that much fuel inside there for the fire to consume so it would burn out quickly.
I was thinking about this again too. I had a computer where the flames exited the case. Sure it was a spectacular bang, but if there had been anything flammable above the computer at the time it would have gone up in flames too.