I have nineteen dedicated 20 amp 10 guage wire circuits for my home theater room, into their own electrical panel to their own copper ground rod, which is then tied to the house ground - this is required both for Code and safety.
I have been told many times of the "potential" problem in using multiple grounds which Carl Holt mentions above.
Knowing Carl Brinkman as well as I do, I suspect that Carl probably ran
4 guage copper wire from each copper ground rod back to the house ground, which I think but am not sure (I'm no electrical expert, I ask others)
would satisfy Code and safety. Whether using more copper ground rods like this might be more likely to cause a "potential" problem, that's another story and I don't know the answer.
I would recommend from I've been told erring on the side of caution (and to keep the cost down, too), with your dedicated audio video circuits running to one copper ground rod, with that rod then tied into the house ground.