The problem is likely to be failing Ram, especially if -
- BSODs occur at random, even when the PC is idle.
- the BSOD messages are also random rather than repetitive i.e. you tend to see different messages related to different drivers each time the PC crashes.
- it tends to occur more often (or can be triggered) when the Ram is in heavy use (eg. gaming).
It could also be a failing hard drive, but that's less likely to cause random system lockups. In that case you're more likely see a BSOD being related to a particular activity or software that fails due to unreadable areas on the drive (bad sectors on the drive). However, a hard drive failure may appear just like a Ram failure if areas of the hard drive being used to store the virtual memory are affected by unreadable bad sectors. Failing hard drives also tend to make a clicking noise at times. To rule out a hard drive failure, do a complete error-checking scan of your main drive (usually C:), making sure to select the option to scan for and attempt recovery of bad sectors. If you find bad drive sectors during the scan, your drive may indeed be failing.
To determine if you have failing Ram, you need to download memory testing software... you can get it here-
http://www.memtest.org/
The site provides an ISO of the software, which you will have to burn to a CD. Then you will have to restart your PC with the disc in the tray, making sure to set your PC's Bios to attempt to boot to the CD before booting the hard drive. The software will give you the option to perform various tests on your Ram and it may take hours so you may want to do this overnight. If you have two sticks on Ram in your PC, you should test them one at a time, so that you can determine if only one is failing. But to be honest, if one is failing and they're from the same brand and were installed simultaneously, you should just replace both (there's a good chance the other will fail soon)
One last thing. If you added new hardware to your PC recently, you should uninstall it to see if its driver was causing the problem. Alternately, you could update the drivers for any newly installed device.