With such a wide variety of string dampeners to choose from I'm often asked by players why use a string dampener? String dampeners do what they are designed to do; dampen unwanted string vibration to reduce arm fatigue. Some players simply can't play without a dampener and others don't like the dampened feel so it's all a matter of preference.
Most dampeners are around $4 so it's worth experimenting to see what brand/style of dampener makes a difference to your game, Just like trying out different strings and tensions for your racquet.
One more thing the correct position for a dampener on your racquet is always beneath the bottom cross-string and between the middle main-strings as shown in the hero image on this page : )