Video cards are being used these days for more than just gaming, with frameworks such as NVIDIA's CUDA and OpenCL allowing general purpose applications to be coded to run on your GPU. If you're just throwing frame after frame of pixels onto the screen, the odd error or two from an overclocked card is going to go unnoticed. But in an applications like Folding@home where precision is a must?
These errors will not appear if you use a GPU stress testing program -- FurMark, EVGA OC Scanner and the like -- but you can test for them using MemtestCL or MemtestG80. Much like Memtest86 does for system RAM, MemtestG80 and MemtestCL make the GPU process a series of repeating patterns, looking for problems in the output.
Both programs run from the command line and can be downloaded from SimTK. Grab MemtestG80 if you have an NVIDIA card, or MemtestCL for ATI cards (thought NVIDIA cards can run OpenCL also). Run the included executable and select "n" when asked if you'd like to submit your card's details. You can if you like, it just means you have to input some additional information about your system.
The tests will then begin. Errors are logged per test, but a cumulative result is shown at the beginning of each batch, so you can leave the program running overnight.
Note that these tests are aimed at making sure your video card's memory is running properly. It's recommended you use it in conjunction with an artefact scanner / GPU stress test to make sure the core clocks are stable. If you find that some games run fine overclocked, but others tend to have issues, this could help find the right memory clock without having to abandon your tweaking efforts altogether.