Component isolation

Damping should be used sparingly or not at all. As Michael states, it does take the air out of the music. IME, lightweight damping may be needed on an enclosed tube component where the cover to the chassis is causing resonance which is picked up by the tubes.
An explanation of one situation.

Also agree with @erik_squires . A component doesn't need to have moving parts to cause vibration. There's internal vibration as well as acoustic caused by sound waves.
As stated, anything with tubes needs isolation and sometimes needs damping using a weight or material on the top of the chassis.
And SS components with large torroidal transformers can suffer from vibration. 

+1 @inna . Each component may need a different footer or isolation solution. And it usually requires experimentation. 

There are many threads in the archives, some recommending an isolation platform plus footers. In the case of certain components like a TT, it's best to use cones or hard footers to drain vibration into a hardwood platform such as maple.