Just a cautionary tale: 4 month ago there was a power cut at 2 am on my street.
In the morning my computer was running although I had it switched off the previous evening. Stench of burned plastic..! And yes, the power cut(presumably) had fried one of my HD and did other untold damage to the Mobo..etc..
The consequece: I have now a brand new shiny silver machine..
My experience is probably not transferrable to all power cuts, but in my case it certainly finished off my machine.