Lots of things can cause a random reboot like that. Typically, in Windows XP or 2000, a reboot for no reason is caused by a Blue Screen STOP error. They are both equipped with an Automatic Recovery Feature that will reboot the system to recover from it. Most systems are too fast to even see the bluescreen, so it just reboots.
To turn off the Automatic Recovery
Start > Control Panel > Double Click on System
In System Properties, Click on the Advanced Tab
Click on the Settings Button under "Startup and Recovery"
And then take the Check out of "Automatically Restart" under System Failure.
This will leave the blue screen up when it happens.
The most important things under a blue screen are the error name, which is a long string of words divided by underscores. Some examples:
IRQL_NOT_LESS_THAN_EQUAL or UNMOUNTABLE_BOOT_VOLUME
The other important part is the stop error code itself, which should be something like this:
STOP:0x00000008 (Whole bunch more)
The easiest way to evaluate these errors is to find the error code or the first Number of the STOP Error, and then search for them on
http://support.microsoft.com. It has an almost infinate amount of help for a lot of errors. If it's something known, there will be a fix. If it's something you can't find there, it's usually caused by specific things. Search for just the error name in those cases, and it will give you some general troubleshooting ideas.