Your octane needs are dictated by the vehicle you drive. Most "performance" cars require a higher octane due to higher compression ratios in the engine to avoid spark knock ("pre-ignition" or "detonation" as it's more commonly referred to). Your owners manual should state the vehicles octane requirements, and it's best to stick to the manufacturer's recommendations. Running poor quality (low octane) fuel can quickly lead to severe engine damage if it's designed to run on high octane gas.
On the other hand, if your vehicle does not require a higher octane rating, you'll gain nothing by high octane gas. As a matter of fact, you may actually lose a little performance and gas mileage.
HTH