Your installed RAM is what comes to my mind instantly, however a dying hard disk can easily cause severe issues too such as file corruption. I'd highly recommend you backup all important files such as My Documents and your web browser bookmarks, etc., to reliable media such as CD-R's or DVD's as soon as possible.
You can test your system RAM with
MemTest86+ which is free. If you have more than one "stick" of RAM installed in your system you need to take out the extras and only test one at a time to see which one "may" be faulty.
Of course the issue may not be memory related, and could be a host of other things from overheating, to other dying components. It wouldn't hurt to download and install
HDTune free version to see what it says about the S.M.A.R.T. status of your hard disk.