Well, system crashes can be caused by pretty much anything from hardware drivers, hardware failures and software applications.
What I would suggest is to "clean up" your OS, using registry analyzing tools like RegSupreme or TuneUp Utilities. Also, uninstall any application that you no longer use. Update you hardware drivers and remove any unwanted services and apps from starting up automatically. Clean up your temp files from the WINNT\Temp and Local Config\Temp\ dirs.
Very important, keep your OS protected with all the securyt updates, AntiVirus and some Anti-Spyware utilities, such as SpywareBlaster and Ad-aware.
Try to document wich applications where running when the system crashed, and see if re-installing them will fix it.
If it's hardware realated, it'll be more difficult to isolate. Sometimes bad drivers can cause hardware to crash the OS, so it'll be smart to check manufacturer's websites to see if someone else is having the same problem as you.
I've never seen RAM gone bad. It'll either be bad from the moment you install it or it'll work. But if you want to make sure, run something like Memtest86 for a few hours.
As for the HDD, enable SMART and use some applications like Active SMART or any other that will display SMART status messages. They'll tell you if you HD has gone bad. Run a full scandisk to check for bad sectors also.
As for the CPU and PSU, you can try running a few hours of Prime95. This app will stress your CPU and RAM so hard that if the PSU has gone bad, it'll shut down.
In most cases, a clean OS install will fix everything (unless it's bad hardware). If your current OS is not stable, it wouldn't be smart to install another one. It could crash even more!
Keep posting!