Depends on the type. You can take both Tylenol and Advil, for example, because one is metabolized through the liver, and the other through the kidneys. You have to be careful, though. Some drugs can't be mixed (example: advil and aleve) and the dosing frequency is different. A pharmacist is a great reference if you have specific questions.
It is not bad to mix the pain-relievers as they serve the same purpose and are also digested at the same time. However, it is good to consult your doctor before you mix them or mix any other type of painkillers.