The only reason to run a higher octane than recommended is to prevent detonation. Higher octane fuel is more resistant to detonation or pre-ignition where combustions occurs before it is supposed to causing severe stress on engine components.
Unless your owner's manual calls for a higher octante or you have modifications such as advanced timing, higher than stock compression or a power adder, there is absolutely no advantage to running a higher octane than recommended.
Some of you mention adding an octane booster and seeing better performance. That is most likely due to the fuel system cleaners that are usually present in those products.
Higher octane fuel or octane boosters do NOT add power by themselves. They will allow you to do things like advance your timing or bump up the boost on a power adder without causing the detonation that would occur with a lower octane fuel.