Seems to be a some misleading info in this thread. A lot of it sounds like placebo and good old "butt dyno".
If your car is rated to run on 87 Octane, putting in higher Octane will do NOTHING to improve performance or mileage (some cars, however, can retard the engine timing to compensate for a lower octane. In that case you may feel a difference). Otherwise, only difference will be that you have a lighter wallet. Higher octane does not mean higher performance.
The octane rating == resistance to detonation. If your engine needs that higher resistance (generally sportier cars, most turbocharged engines), then you need higher octane fuel because engine detonation is bad, mmm k? If you run 87 in a car rated for 91 or 93, there's a high chance you hear pinging, etc.