For starters, what do you do about spyware and viruses? Anything, nothing, something, what?
If you rule those out, then heat is often a culprit. Check your computer to make sure the fans aren't clogged with dust and that they're still spinning when the system is on. You can also try running the system with part of the case off to see if that helps things at all.
The final possibility seems unlikely given what you describe, but the power supply could be the problem. USUALLY if it's a power supply thing, it'll only happen when you do something that needs a lot of power, like starting a game. Of course it's possible your power supply is a bit dodgy and so sometimes a slightly bigger than normal dip or surge in the mains power will make it unsettled. If that's the case, it's pretty easy to replace a power supply, since the plugs all really only fit in one place. Either way, investing in a UPS (Uninterruptable Power Supply) with AVR (Automatic Voltage Regulation) can pay off significantly.
Your computer wants a nice steady sine wave of power. That doesn't happen when you're plugging into wall outlets. There are various dips and surges happening all the time. Over time, this takes a toll on a computer's power supply. A UPS with AVR will sit between the mains and your computer and do whatever's necessary to deliver that steady sine wave to your computer, which can significantly increase the lifespan of a computer.
What does it mean when a computer starts to restart itself at random times?
My computer has started doing this recently...Sometimes it will do it when I try to open a program, but there are other, less predictable times...like when I'm in the middle of writing an email...or when nobody is touching it at all.
I'm using Windows XP, with a pentium III processor...(I'm not really sure what kind of system info to put...i'd have to look up a bunch of it, cause i'm technologically handicapped...)
What could be causing this? is it software, or hardware? I'm not even sure where to begin for looking for the problem...