When recording I prefer not to dampen anything, however it depends on the kit that arrives. The number of times drums turn up with old skins, out of tune (completely), tons of tape and muck, never ceases to amaze me.
If I do have to dampen a drum due to it being impossible to tune, as it has been over tightened all its life, I usually place a small piece of Gaffer tape on the bottom skin. I fold the tape so that it has some weight but does not take up too much surface area.
Another tip is on the snare, if it has a lot of ring (which is not always bad) and the ring does not suit the track I place a very thin and narrow dead ringer on it to tighten it up.
I find the best thing inside a kick is a small blanket folded neatly in the bottom just touching each skin, some drummer insist on having nothing, this is fine if they have the drum set up and tuned correctly for the sound. I hate kicks that turn up stuffed full of pillows, how the hell is that supposed to sound good?
Cheers
Alan.