This is a stupidly IMPORTANT skill for ANYONE playing guitar... doesn't matter if you play electric, acoustic, classical, with gain on 10, jazz comping only, gypsy-shred, low-E-only-riffing...
I've met too many guitarists who can't keep the rest of the guitar quiet while they do their thing.
I think its a lost discipline... and a by product of sloppy, indifferent practice. I don't understand how one can get by it when you have ringing, clashing notes all over the place?
Actually, dampening is an art and its quite personal. Look at EJ's way of doing it then look at Marty Friedman's (apparent lack of) dampening. Interestingly, I find that THE WAY to proper dampening can only be discovered by the player himself. Its like trying to tell a player to hold his pick in only ONE POSITION - which doesn't make sense. But what makes sense is the outcome, the end product.
So I'd actually suggest being critical, listening carefully and even recording oneself in practice - extra noises = poor dampening so please please please, re-look your technique! You are either the best critic or the most ignorant hobbyist...