As mentioned there could be several issues that could cause this. I saw Andy A's post mentioning a component heating up and it reminded me of a similar issue I had.
One of the computers I have is an AMD-K6 500mhz that was custom built 3 or 4 years ago. The computer worked fine for a 1 1/2 years but then started randomly rebooting. It could do this several times an hour or not do it for a few days. After making sure all the fans were clear of dust, deleting software and swapping out components to no avail I finally removed the fan from the chip, cleaned both surfaces and readded heat sink compound between the two. To this day the computer has never acted up again. I can't say this is your problem but something you might want to possibly check.
The suggestion to run the Ad-Aware software is good to. I have it on all my computers. Another freeware program I have on all my computers is SpyBot-Search and Destroy. I don't have a website off hand but it should be easy to find.
I found the website for it, link is below.
http://www.safer-networking.org/index.php?page=download