Benchmarking tools abound, but FurMark was designed specifically to give your GPU a stress-inducing workout and punishes graphics cards much harder than the average game. This bad boy uses real-time renderings of furry objects undulating in front of groovy backgrounds to push your graphics card to its limits, complete with antialiasing and resolution options. Stick to the standard burn-in test, but keep an eye on HWMonitor and/or SpeedFan--FurMark gets your GPU very hot, very quickly. You won't need to run FurMark for long. If your graphics card is going to crash or start tossing out funky visual artifacts, it will do so within 15 to 30 minutes.
Alternatively, Uningine--the makers of the popular Heaven graphics benchmark--recently released "Valley," a new GPU stress-testing tool that's a lot prettier and more peaceful-looking than Furmark. I haven't had a chance to use it extensively, however.
Once your GPU passes its primary stress test, I like to run some benchmarks derived from actual games to see how the graphics card holds under real-life usage. My favorite software for doing that is the Alien vs. Predator and S.T.A.L.K.E.R benchmarking tools, both of which are freely available.
What about the rest?
The CPU, GPU, and RAM are the only major system components you really need to worry about stress-testing. Should you benchmark your storage drives to make sure they're delivering the promised data transfer rates? Sure--but that's a performance issue, not a stability or reliability issue. I recommend checking a new hard disk drive's health using a S.M.A.R.T. monitoring tool, but that's about it, the usual "Make sure your data is backed up!" axiom aside.
Likewise, you can loop a long video with your display brightness on high if you're worried about the battery life of your laptop, but again, it's far from necessary and more of a benchmark test than a stress test.
While this guide can help ensure the stability of your system, the methods and tools outlined here are far from your only option. In fact, a plethora of different stress-testing strategies and software solutions exist out there in the wild. How do you stress test your PCs?