Positive displacement pumps are divided into 2 classes: rotary and reciprocating.
Rotary P.D. pumps such as screw, progressive cavity, lobe, peristaltic, gear pumps emit almost no pulsations, therefore do not require dampeners.
Reciprocating P.D. pump such as piston, plunger, axial piston, diaphragm,etc. transfer the rotational motion of the driver into back and forth motion in the fluid end. The more pistons/fluid compartments there are, the smaller the pulsation is from each.
As prior posters said, the answer to your question is dependent upon the individual service and installation. If your system is robust enough to withstand pulsations, then don't use a dampener. If the pipes start shaking bolts loose, then use one.
Pulsations will not hurt the pump, only the system or process.