All electrical codes that I know of specifically state that every electrical service must be grounded at the source (utility) transformer and that all equipment grounds must terminate at that point. In other words, there can only be one point that ALL grounding conductors or grounding paths terminate, and that point is usually the house water main or ground rod. The water main/ground rod is connected directly to the neutral bus of the main service panel which in turn is connected to the utility transformer ground.
This does two things: first, any surges, static or spikes from lightning are dissipated. The utility transformer completes the circuit from the house ground to the transformer ground which permits the energy to be dissipated into the earth. If you place a second ground rod at any circuit as Elescher states above, then what could happen is that the energy from a lighting surge will be short-circuit to the second ground rod (away from the utility transformer) and the surge will backfeed into that receptacle, frying anything connected to it.
Second: if you place a seperate ground rod at a receptacle and there's a fault on the equipment, the circuit breaker may not trip. The ground rod will have a resistance, say, of 25 ohms. A 120 volt fault will cause a current of 5 amps to flow (120V/25ohms) - not enough to trip a 20-amp circuit breaker but enough to be dangerous to the touch. If you touch the equipment with one hand, not a problem. But with two hands, the space between your hands is a conductor and you will get a jolt. That's why most sensible amp technicians never put both hands inside a live amp chassis.
Bottom line: add the extra ground at your own risk. Illegal and a tad dangerous.