As the title says really - I think it would be helpful to have a sticky in here detailing stability testing - things to test, programs to test the with etc. Unless I'm being blind I can't see anything like this here and though I know it's been covered a lot in individual threads here's my 2p:
There are two root causes of instability - hardware and software.
For software related problems this can be:
Bad / mis-configured drivers
Mis-configured OS
A virus
For hardware related problems this can be down to:
Faulty hardware (commonly RAM)
Overheating
Undervolting (i.e. PSUs output is low or has too much wobble in the lines under load)
Or (if overclocking) that you've simply reached the ceiling for that CPU / RAM without being able to provide more power and / or more cooling
Good programs to test if you system is stable are:
RAM:
CPU / RAM:
GFX / CPU / RAM / system testing:
Any more suggestions?