Timtim,
As has been said, it is essentially an absolute must to have a ground rod at the service entrance, that serves ALL runs. For reasons of code compliance, effective circuit breaker operation, lightning protection, etc.
No one in this thread has advocated independent ground rods for each line that is run to the system. And I think that Jea has effectively made the case that having even a single ground rod dedicated to the system is pointless, as well.
The question of tying the dedicated ground runs (not rods) together at the system is a little less clear cut. As I indicated earlier, there is both potential upside to keeping them separate (improved isolation) and potential downside (offset voltages between chassis causing noise currents to flow in common with signal returns).
That downside would pretty much be negated, I think, in the case of a system that had balanced interconnects. But most systems have some or all of their interfaces single-ended. For those cases, I am not in a position to offer generally applicable guidance as to whether the upside or downside is more likely to prevail. It could be that trial and error is the only way to tell in a particular case. And as I said earlier, a more ideal solution would be to make use of isolation transformers as discussed in the other thread I referenced. It seems pretty widely agreed that both the isolation they provide and the filtering that results from their limited bandwidth make them a very effective approach.
Regards,
-- Al