Computer hardware is not perfect; manufacturing errors do still occur, and parts that once worked fine can develop problems over time. These problems may not be as obvious as a system that simply fails to work. A variety of CPU stress testing software exists to help weed out bad systems and identify those that work properly. The testing typically performs long and grueling mathematical calculations, exercising every part of the system and alerts the user upon any failure.
Prime95 for Windows and its Linux equivalent, MPrime (playtool.com), are popular and free Mersenne prime number search programs. Seeking prime numbers is an intense and time-consuming process that requires precise calculations. Prime95 and MPrime will halt and alert the user if any calculation fails. They come with a "torture testing" mode specifically designed for putting your computer's hardware through its paces and can optionally contribute your calculations to an Internet-wide collaborative effort to find new prime numbers.
System Stability Tester
For the open source geek in you, there's System Stability Tester, available for both Windows and Linux (sourceforge.net) this free program uses your hardware to calculate the number pi to millions of places using several different algorithms. Their results are compared, and any discrepancy is reported to the user.
CPUBurn is another free and open source project that runs on Windows and Linux. This program is designed to cause your CPU and other components to emit as much heat as possible rather than strictly to check for calculation accuracy, as a way of stressing your ventilation and cooling systems. Be sure they're in order before running this one.