This could be a problem with Windows, in which case a clean install should help. It could also be a problem with the video card, CPU, memory, inadequate power supply, overheating (which may also cause re-boots and lock ups)...

From "Crashes, errors, & hesitates, all the time" my first suspicion would be Windows or memory. Does this only happen in games? Do you have any other programs that stress the system (3D modeling, video rendering, or opening 30 programs)?

There is a memory testing program that is easy to use (run a batch file to write the program to a floppy, then re-boot and let it run for awhile (over night should be more than adequate, but it is a very thorough program; I left it running for 2 or 3 days on 512MB of PC133 once).
http://www.memtest86.com

You could try installing 3DMark and looping the demo for awhile (perhaps over night).
http://www.futuremark.com/download/

There are a few overclocking sites which will have FAQs and links to programs designed to test the stability of a CPU or stress test the system, which would work just as well for testing a non-overclocked computer. If you don't want to read a bunch of web sites and newsgroup posts, and don't know anyone who could take a look at it if you invite them over for dinner, you could consider taking somewhere to be serviced (depending on how thorough they are, they might assume it is a software problem and want to charge you a couple hours labour to re-install windows; make a backup first, in any case).