Well there was a power cut here just now, but fortunately the UPS I bought a few months ago saved the day, so while you wouldn't have been able to connect for about half an hour the server remained up, so we haven't lost any progress.
My plan in such events was to take the screen from my main computer and plug it into my old computer, but it looks like I don't have a spare power cable that can plug from the screen to the UPS, so until I get my hands on one (hopefully when I'm in auckland in a couple of months) any power cut that goes long enough for the UPS to run out (30-60 minutes I think) will take down the server.
This was a close one... the 'oh noes the power is out!' beeping sound the UPS makes sped up, which I assume means it almost ran out of power.