During rendering the computer turned itself off.
So I tried a second run, this time with all other applications closed. The computer turned itself off another tome.
Is this normal behavior?
Only in the Twilight Zone. 
I had that problem once, and it was an overheating CPU chip that went wonky when I put it into high gear (like doing a render). Is your computer old, dusty, or overclocked by chance?
My computer is three years old now and not overclocked.
I’ve had this shutting down issue once before during a scan of Spybot Search and Destroy.
This may not be blender’s fault…
If you’re trying to render a very large scene it will require a lot of processing power. A lot of work may heat your CPU and there is a feature on modern PCs to shut down themselves if the CPU gets overheated to prevent it from melting. If your CPU is overclocked that may also be the reason why it’s unstable (overclocking makes the CPU work faster than its factory settings and thus heat much more much faster…)
Give us some more info about your system so we can figure out what’s the problem easily…
EDIT: Whoops! I’m a slow typer…
My old computer had problems with rendering also- either replace the processor or lower the resolution.
My computer has a 2.4 GHz. Intel Pentium 4 processor and 512 MB RAM.
The resolution I used was 400 x 300
If you’ve never had the cover off, it could be dusty inside. Feel the back of the computer when it’s running… there should be a good breeze coming out from the main fan. If not, there may not be enough cool air getting to your CPU. Run it with the cover off, and make sure the little fan on top of the CPU (assuming there is one) is running, too. With the cover off and with the computer powered down, try spraying the insides out with some canned air, and especially get the inside of the power supply. Those steps may help.
About 6 month ago the CPU ventilator was replaced. The repairmen also cleaned the area.
Also a good breeze can be felt at the backside of the computer.
Hmm… off the top of my head, then, I’m not sure. The problem you describe certainly sounds like the CPU overheating. However, the root cause of the problem may be more complex. There may be a problem with the new CPU fan, or the chip itself, or even the case design. I’m afraid you may have to have a repair person look at it again, to be sure, though. Sorry I couldn’t be more help.
It really sound like it’s overheating during rendering. Open your computer case, check for dust on the CPU heat dissipator (is this the right word?) - the thing under the fan. If dust covers it up, then the processor doesn’t cool down enough. I had that problem too - dust kept my processor from cooling: before cleaning it a bit, it reached about 80 °C with simply Mozilla running (yes, it was really clogged).
Get a Mac
My iMac has never crashed, turned itself off, overheated, or infact done anything wrong.
It solves everything.
Is that like, “get a horse?” 
Check this out:
http://www.annoyances.org/exec/show/article07-200
Add “changing video card drivers” to that list if you have an NVIDIA video card. I tried to install their latest drivers and had nothing but trouble - apparently you can’t trust their installer to remove all traces of the previous driver so you have to uninstall the old driver, run some 3rd party program to do what uninstall didn’t (from safe mode no less), THEN install the new driver.
I make no guarantees, but if you think it’s your vid card (updated drivers lately?) the 3rd party uninstaller can be found here:
http://www.drivercleaner.net/
Its overheating protection.
Clean up the processor cooling block & fan, and all the fans and airways of the compu case.
The only other reason would be malware on your windows, but not sure if you on windows (if you are, test running blender on kubuntu).
People here seem to like the heat conclusion so it should be noted that some newer computers have alarms built in that let you know the temerature has reached a “warning” limit before it shuts down. Mine emits a constant tone from the pc speaker and maybe the hard-drive light flashes too.
Anyway, if your motherboard came with any software it probably has a temperature monitor you can check… my machine is about 5 years old but the monitor software still shows MB temp, CPU temp, 4 fan speeds, voltages for each power supply. All that information can be logged to a file in situations like yours. If the software isn’t already on your machine, check the installation CD for your motherboard or go to the manufacturers web site. Old computers might not have this functionality but I can’t imagine that a newer computer wouldn’t.
I’d have a look at the temp monitor before I popped that case open, mostly because I’m lazy that way.
Living with 3 dogs in a porous house surrounded by corn fields gives one a unique perspective on the cleanliness of computer innards. In my spare time I make sweaters from the fluff found in my tower… then the dalmation eats them so she can sh!t 'em out in the back yard.
Good luck.
I’ll go back to the repair people to check the CPU overheating problem.
bah! You should save yourself the time and money by checking that monitor - it’s a piece of cake.
I could not find the CPU temperature monitor on my system (Windows XP). So I have the intention to ask the repair people where I can find this monitor. Tomorrow I’ll go there but without my computer, just to get information.