Mustang, thanks for your patience with me!

Each building needs a ground rod. It can have more. All rods, and all panels, have to connect to it in some manner.
If you had one panel into the building, that in turn fed the other panels, then only that first panel would need to be connected to the ground rod.
If you had two feeds coming into the building, both panels would have to tie into the ground rod, Ufer, etc.

You're right about one thing, though...I got the NEC backwards as to GEC size. For NEC, #6 is "max." while our local rule is #4 "min."

Far be it for me to quibble with Stallcup, but I point out that a number of countries...Norway comes to mind...do not use ground rods, etc. Last I saw, their industry was just as modern as ours. That is- and I stress this- as long as we are talking only about the ground rod and the wire to it from the panel.
In another sense, though, it IS essential to "ground" your system; that is, have a "grounded conductor" or 'neutral'. Simply put, really weird things, including large transient voltage surges, can occur as loads change on the "hot" circuits, unless there is some point where the different feeds (transformer windings) come together.
How can this happen? Well, imagine a 240 "delta" system. Should a short happen, there would be a 208 volt to ground potential. Yet, your transformers are isolated from ground. The result of this is a wildly varying load on the windings, heat, etc. Yet, if you deliberately ground part of the delta, you can control the system, the windings can 'stabilise,' because there is a nice, clean path back to the system.
Put another way, a completely ungrounded system is esesntially a system where all loads are in "series", rather than "parallel," so changes in one load greatly affects the others.