Originally Posted by Blameless
Personally, I generally test with the following:
LinX (with the latest Intel Math Kernel Libraries), set to a problem size of 20-25k for basic CPU/IMC testing, and seeing if your cooling is up to a worst case scenario. IBT is similar enough (same binaries, different front-end) that you can use it instead, if you prefer; I just find the LinX interface more useful.
Prime95 Small FFTs for more core testing and custom Blend (8 to 2560k FFTs size, 5 minutes per test, set to use 80-90% of your physical memory) for memory and IMC testing.
HCI Memtest for Windows, for testing memory stability. Use one instance per logical core, or 1.5 instances per physical core, whichever is greater (e.g. 12 instances on a Gulftown, 8 on a 2600k, 6 on a 2500k, 9 on a Thuban, etc). Have each instance use the same amount of memory, with the total memory used equal to 80-90% of your physical memory. 2000-5000% seems to be a good test duration.
OCCT GPU test for core/shader clocks. I use shader complexity levels 1 and 3 on NVIDIA cards and 1 and 8 on ATI cards (which tend to be more shader heavy). Causes extreme GPU and VRM load, so is good for worst case scenario thermal testing. It also has an artifact scanner that will find most errors at lower clocks than you will see them in game. Some people are extremely anti-OCCT, but as long as you keep an eye on temps, don't have a card that was defective out of the box, and don't use stupid levels of GPU voltage, you'll probably be fine.
FurMark, just to get confirmation of stability from a second test.
Crysis GPU bench on loop, or looped 3DMark can use much more VRAM and can thus find VRAM instabilities OCCT and FurMark may overlook.
In addition to these individual tests, I use combinations of these programs to better simulate real worst case total system loads. FurMark is especially useful to run in the background as it has almost no CPU utilization, so can be used to dump tons of heat into the case near the CPU and memory, while you stress test the CPU/RAM with another program like LinX or Prime95. It will also heatup the chipsets on most boards, which can reveal errors with them.
I'm actually trying a new OC right now, and have Prime95, FurMark, and ADIA64s disk bench all continually stressing every major subsystem while I poke around the internet.
Anyway, this list is far from comprehensive, but is a good sample of the programs/procedures I've personally found most useful to produce and isolate errors.