The risk here is if your power supply develops a "case-to-live" fault in which a short circuit is made between the live pin and your case.
In this condition if you had the third pin (the earth) connected it would simply short to ground and blow the fuse or trip your circuit breaker and would be nearly harmless.
Without the third pin in the plug connected there is no connection to earth and it is potentially possible for your case to become live electrically for some period of time and once you touch it or brush against it you could get a severe electrical shock. Chances are this would destroy the electronics in your computer as well so you'd probably notice it had stopped working first, but then that would make it more likely that you would then check the power connection and thus electrocute yourself.
Chances are that unless you have an RCD installed at your circuit breaker that you would give yourself a very serious shock before the fuse blows. The RCD would would help to protect you, and you'd live to regale your friends with the story of how you nearly electrocuted yourself, but would still mean that you could get a shock that you would certainly remember for a while.
Granted this condition should be very rare, but there is still a chance of it happening.
The third (earth) pin is there for a reason. If you can, use it.