I would have to second pretty much everything that chawk_man said. But, for more in depth clarification of his statements, here are a couple of facts:
A gallon of "regular" or 87 octane fuel contains approximately 111,400 BTU of inherent energy. Care to guess what a gallon of "premium" or 92 octane contains in the form of energy? No need, I'll tell you. The answer is; approximately 111,400 BTU!
So, it is clear that there is ABSOLUTELY NO power advantage to using a higher octane fuel. You can't squeeze any additional power out of a gallon of premium than you can a gallon of regular.
The ratings, or numbers, associated with "quality" for regular and premium gasoline are pretty much universally derived from the amounts of particular types of hydrocarbons that are used to formulate each fuel. Basically, the two hydrocarbons used to obtain the "ratings" are isooctane (C8H418) and n-nepthane (C7H16)
Simply put, (because that's all I understand anyway) n-nepthane is a hydrocarbon that is somewhat volatile and ignites readily without much "persuasion". Isooctane, on the other hand, has a tendency to be a little more difficult to ignite and, once it does, will burn slower and "smoother" in a very contained and predictable manner.
Staying with simple here...87 octane gas will contain a mix of 87% isooctane and 13% n-heptane. While, on the other hand, 92 octane, "premium" gasoline would be comprised of 92% isooctane and 8% n-heptane.
And, like chawk explained, this is all done to address the issue of detonation that can take place in higher compression engines. The "smooth predictability" of the isooctane is important for a flame that has a tendency to advance consistently throughout the combustion sequence rather than sort of "exploding" and causing the kinds of undue pressures within the cylinder associated with "pinging" and detonation. A sure engine eater if allowed to happen for extended periods.
The bottom line is that it is a waste of money to run a higher octane fuel in an engine that does not REQUIRE it. There is just no useful data to suggest that there is ANY advantage to using a higher octane rated fuel but there are some people in the industry of engine performance that would tell you that there may actually be some DETRIMENT to unnecessarily using a higher octane fuel than you need.
Cheers, and thanks for bringing the subject up.