Thanks everyone for the info! I only wish I knew as much about this stuff in order to return the favor.
So, I checked my breaker box. My living room, where I would install an amp (let's say a Rotel RMB-1095, for argument sake), is on one 15 amp circuit. In other words, it appears that my wall outlets and lights in the living room are on one single 15 amp circuit. If I were to install the RMB-1095, it would be added to that circuit.
I am assuming that since my breaker is 15 amp and that since my house was built with the cheapest materials in the housing business, that my electrical wiring is matched to the 15 amp breaker (ie, it is not thicker than it needed to be).
Rotel tells me they "recommend" a dedicated 20 amp circuit for that RMB-1095. Given my situation above, I think I would be taking a bit of a risk, if not a safety risk, then certainly a risk that I might trip my breaker everytime I try to use a $2,000 product. That, of course, would drive me nuts.
I believe I am correct in further assuming that changing my outlet to a 20 AMP plug, while leaving the existing wiring and leaving the 15 amp circuit breaker is not a real solution, only a partial solution that will not guarantee a trip-free experience.
Or, would I be OK with a 20 amp outlet, but keeping the existing wire and exisiting 15 amp circuit? Our house has no basement or crawl space, so re-wiring is out of the question.