This could be a huge-alternate thread, so I won't get started, but put simply, higher octane allows the engine to run greater amounts of timing advance without knock.
Octane by definition is a fuels resistance to detonation (AKA knock). Most cars are DESIGNED for 87 octane, so they just don't advance the timing any further than that fuel requires ( and thus don't reap the benefit in power and efficiency it affords).
Now, cars that are DESIGNED for high-octane fuels (ESPECIALLY turbo and supercharged cars) NEED high octane fuel to achieve the performance they are rated at. If you use lower octane fuels they engine computer will pull back timing to prevent detonation, and as a result you won't get the power or mileage that you expect.
If your car calls for high octane fuel, then using it will benefit you and the car (and don't think you'll save money by using low octance fuel... the reduction in mileage as a result of the reduced timing will MORE than outweigh the difference in fuel price).
In short, use what the manufacturer recommends! They kind of know what they're doing!
Oh, and I want the LS3... screw the L76 and all its truck based hardware! Corvette power if I can get it!