Lately I started to leave my computer on overnight. I let it scan, defragmentate, download stuff and I also leave my music on (I like to sleep like that). But the think is, that somedays, like once every 2-3 days, when I get up, my PC is shut down. I don't know why or when it happens. It never happened while I was up, only when I'm asleep.
I also have a bad power outlet, so it might be that, but I don't know for sure. Do you guys have any ideas?

hmm strange, maybe power variation shut it down.

Or windows update

Or power supply is failling.

Or virus.

Or hacker.

or windows is self destructing.

But you should shut down your comp at night, save power.

The only potential damage shooting down you comp may do to you comp is the thermal change that change the density of the metal composing your comp. in clear not much danger there.

While leaving it open let it available to many evil thing that may happen on the web...

One of your parents sneaks in your bedroom while you're asleep and shuts down your pc?

Well, automatic updates will restart your computer if they are important, but normally only after for my computer with vista is at sleep for something around 4 hours.