The "third-wire" ground is specifically for safety, where ever an appliance has exposed metal that could potentially be made "hot" by an internal fault. In other words, anything with a power cord running into it, and metal on the outside. The ground wire is electrically the same as the neutral wire from the AC line, but provides a redundant pathway that is there to insure that the metal remains at ground potential. If there is a fault internal to the appliance, the ground path connected to the exposed metal is designed to blow a fuse or breaker.
That's the sole purpose of the third wire. Current code allows for the elimination of the third wire ground on a device where insulation standards are such that the possibility of any exposed metal parts becoming electrically hot meets a certain threshold of improbability.
The third wire ground was added after enough faults happened and enough people got shocked that the code was changed. This happened often enough with electronic equipment, since it was often desirable to have the metal chassis double as the signal ground and to have signal ground referenced to the AC line. Since the equipment often operated just fine no matter what side of the AC line its signal ground was referenced to, it was only a matter of time before a two-prong plug was reversed and a chassis became "hot". The first attempt at preventing this was the "polarized" two-prong AC plug, where the wider of the prongs was always to be the neutral side of the line and signal ground was always referenced to that side of the line. Unfortunately, this system relied on outlets that would accept the polarized plug, and that were wired correctly by whomever installed them. It also relied on consumers never altering the plug to fit into an older outlet.
Needless to say, people still managed to find a way to get shocked! Hence, the authorities decided to make the system a bit more fool-proof by adding a whole separate safety ground. Of course, consumers have still defeated this whenever they found it inconvenient!
Where this impacts audio equipment has to do with the various paths the safety ground may take on its way to the common grounding point back at the service entrance. Two different grounded outlets may take paths back to this point that vary widely in where they run and how long they are. This means that the two safety grounds may be at a very slightly different potential relative to one another. So, if two pieces of gear with their safety and signal grounds tied together internally are plugged into these two different outlets, their two signal grounds can end up having that same small difference in potential. If they are also connected together by an unbalanced signal patch cable, then this difference in potential, small thought it may be, is indistinguishable from an audio signal at line frequency.
An easy way to avoid this in a home setting is to, as suggested, have all your audio gear plugged into the same power strip. Only one ground path that way.
The important thing to keep in mind is the different purposes that safety-ground and signal ground are there for. That they are often connected is confusing, but they really are two different things.
