Testing Memory:
A common program is called memtest86. This will detect any memory errors, and can aid in diagnosing any bad sticks. Memory errors can be responsible or anything from a crash, to strange behaviour.
http://www.memtest86.com/
Testing Processors:
Prime 95: This program will torture test your machine by having it crunch numbers, lots of them. If a machine can pass this test for hours, chances are the power supply, processor and motherboard won't be the cause of the problem.
http://www.mersenne.org/prime.htm
Scanning for video artifacts:
Ati Tool: For both ATi and Nvidia cards, this will tell you if your card is producing artifacts, whether you can see them or not. (many times a card can produce artifacts, yet they're so minor you won't notice them) Although it is a very nice overclocking tool, i don't mention it here for that reason.
http://www.techpowerup.com/atitool/
Diagnosing overheating:
Generally speaking, if your computer is overheating, it most often will crash after a certain length of time. Often this time can be approximate. Such as about every 30 miniutes, or about every 2 hours. These can be some of the most time consuming to diagnose, since they can take so long to show up.
A good test to see if your computer is overheating, is removing the side of the case and seeing if that lengthens the time, or eliminates the crashes. (of course, only do this if you're comfortable, spill a beer in it and it isnt my fault
) Why do that? Well, you can still play games while the side if off
Instead of starting at prime 95 run for 6 hours. So what do you do if it does appear to be overheating? Well the first thing is scan for dead or failing fans, large clumps of dust, or other out of place things. If a video card is overheating, chances are you'll see artifacts, or other video weirdness. (cards that are failing can also do this)
Processors that overheat tend to lock up the machine, or cause reboots. Memory generally does not overheat. However chips on the motherboard can, so keep an eye out for north or southbridge chips that have failing fans. (generally north)
Leaking or failing capacitors can also cause erratic behaviour. I don't have a handy picute, but caps start to mushroom generally when they begin to fail. They look like cylinders and are all over a motherboard, if the top isnt flat, it may be getting ready to go.
Memory problems:
These can be a huge pain the butt. Often bad memory makes itself known at random times, or the worst possible time. Sometimes memory can appear to function fine with 5 games, yet on one game it craps out at a certain point. Oh the joy of bad memory
Luckily though, memtest will pick up bad memory, you'll just need to let it run for hours. If you suspect memory, you'll need to follow the directions at their site and give it a go. Software problems:
Yet another cause of problems can be software. This can entail virii, spyware/malware, and driver problems.
Virus': Grisoft offers a rail anti virus from their site. It's functional and non intrusive. It's a nice program if you think you may have a virus.
http://www.grisoft.com/doc/1
Spyware: An old staple is spybot. It's still well done and very effective. Although you may need to be in safe mode for it to remove the really nasty stuff.
http://www.safer-networking.org/en/index.html
Be sure your computer is clean, and your drivers are up to date. However, especially in the case of video cards. The newest driver may not be the best in your case. You may have to experiment.
Sometimes a windows reinstall will be needed, if you aren't comfortable doing it, you may want to take it to a shop, or get your geeky friend to do it.
So theres some information i hope helps a few people. Feel free to add to this thread as this post is not meant to be an encyclopedia on troubleshooting.
just a few tips and hints. I may add to this thread if time permits.
I use that, and Hijackthis, religiously. 
