Every CPU since the 486DX-66 has been outfitted with a heatsink or a heatsink and fan combination simply to keep the die-temperature within operating limits. Back in the days of the 486DX-66 we used a heatsink that's now just about adequate to cool a videocard or a motherboard chipset and we've come a long way since then. Modern CPUs such as the Pentium 4 and AMD's Athlon dissipate up to 70-watts under full load and requires more than a just extruded piece of aluminum and a small fan to keep them from running too hot.
Fig 2. An Intel 486SX-25 CPU, one of the last Intel CPUs that could do without a heatsink.
And quite frankly that's were the culprit is, as modern CPUs need a powerful cooling solution to keep them running within functional limits. As operating outside of these limits, i.e. the CPU getting too hot, will quickly cause the system to display erratic behavior such as lockups, freezes, random reboots but can also cause the CPU to become defective. Naturally a system integrator or computer hobbyist building a computer will go to great lengths to ensure that the CPU and the other system components are adequately cooled so as to prevent any damages or erratic behavior.
CPU manufacturers have naturally also built in certain precautions to make sure that if the CPU runs too hot the user is notified or the system actually goes into standby or powers down. Or at least that is what Intel does with their Pentium III and Pentium 4 CPUs, as they both have an on-die thermal diode and protection circuitry that monitors the die-temperature. AMD however has not yet included a thermal diode or thermal protection circuitry with their current line of Athlon CPUs, a feature that will be included with the Athlon 4 CPU though.
However, not only the CPU manufacturers have implemented features to monitor the CPU's operating temperature, motherboard and chipset manufacturers have also come up with ways to safeguard the CPU. Most Athlon motherboards, for example, feature a thermistor mounted underneath the CPU to measure the CPU's temperature as well as a fan monitor that keeps an eye on the CPU fan's RPM. Intel motherboards have the same features although they usually do not have the thermistor mounted underneath the CPU, but rather get their CPU temperature readings directly from the on-die diode.
But even with all of these precautions a CPU will only be able to work properly when a CPU cooler is installed that is capable of handling the heat load the CPU will be dissipating. Furthermore the CPU cooler must be able to extract that heat from the CPU-die to the heatsink material quick enough. The reason we see copper-inlay or whole copper heatsinks more frequently is the simple fact that modern CPUs are getting smaller and clocked higher than previous generations. As a result the heat generated in watts/mm^2, or simply the amount of heat dissipated from the CPU-die is much more than we used to see with older CPUs. A straightforward approach with an extruded aluminum heatsink and a fan simply isn't always capable of getting the heat off of the CPU quick enough to guarantee that all parts of its CPU-die will remain within functional limits.