After a long while the thermal compound can cause the cooler to stick to the CPU. If you are trying to remove a cooler from an old CPU, you may want to run a CPU stress testing utility like Prime95 for a bit first to warm up the CPU, loosening up the thermal paste's hold, then shut down, unplug the computer, and remove the cooler. Using a hairdryer to warm up the thermal compound may also work, but you would want to be careful with that, as that may cause electrostatic discharge, which could fry your components.
Just be careful when pulling the cooler off of an older CPU, if it isn't budging, warm it up first, and try again, do not try and yank it with full force. Removing the cooler and reapplying thermal paste regularly can also...