The Red Hat 9 Linux on my computer does not do that. The only time it ever locked-up was once while I was trying to post a message saying how it never locks-up. It has almost never happened. When it did that one time, I pressed the CTRL-ALT-BACKSPACE keys simultaneously which took me out of Gnome and back to the Linux command-line interface which was still working perfectly. I then typed startx and was able to quickly restart Gnome.
This is just a wild guess but have you tried testing you memory? Below is a link to a free program which will test it for you. On that page it list a Linux version and a Windows/DOS version. I used that program once about 6 months ago and it said my memory was ok. I ran the DOS version of the program from a bootable floppy disk.
If your memory is ok, I am not sure. Back in the days before plug-and-play two devices trying to use the same interrupt at the same time could cause stability problems. I do not know it that still happens much any more or not? With Windows 9x, bad or incorrectly configured drives could also cause problems. I suppose that could happen with Linux too. Do you have any other operating systems such as Windows installed and are they stable? For me Linux was usually the one that was most stable.