Yeah, I put in 93 once and had a small but noticeable increase in power. From my understanding, this only really happens if your knock sensor is retarding your timing with 87 octane and 93 lets it advance the timing further. It's 87 minimum, 91 recommended with my engine.
Since I secretly wish my car was a small diesel, the slight lack of power with 87 doesn't bother me too much :)
Now that the price difference between 87 and 93 is typically under 10%, using 93 may actually improve your gas mileage enough to make up for the difference in price. If your drive enough that fuel expenses are meaningful, it may be worth testing if this is the case for your car.
Another note I've learned on higher octane gas: in areas prone to freezing temperatures (I live in the northern Midwest), 87 octane will, during winter, have ethanol added into the mix as an anti-freeze. This is commonly called the "winter blend", and is federally regulated to only be on the market during certain times. The ethanol has lower energy density than gasoline, and can hurt your mileage. Higher octane gas does not have extra ethanol added in. So there's a benefit to using midgrade or premium in cold weather.
Compression is fixed by the engine design. The only thing the ECU can do as a result of knock sensor input is retard ignition and close the throttle (and, on a turbocharged engine, lower charge pressure).
Retarded ignition does result in lowered gas mileage, but throttling down does not. It just decreases your maximum available power.
Plus, if you notice the decrease in power, your driving is not suitable for comparing gas mileage... ;-)
The maximum possible compression is, yes, since it is determined by the size of the cylinders and the piston stroke.
But retarding the timing amounts to reducing the effective compression--basically you are wasting some of the compression that's available by delaying the spark until the cylinder has started expanding again. I should have made it clear that it was effective compression that I was talking about.
Since I secretly wish my car was a small diesel, the slight lack of power with 87 doesn't bother me too much :)