In general, No.
It is a common misconception that higher-octane (premium) fuels improve gas mileage. Octane rating has nothing to do with the energy-content of the fuel. A fuel's Octane Rating is simply the measure of the fuel's resistance to auto-ignite (ignite under pressure without spark), also called 'knock' or 'predetonation'.
In other words, premium-grade fuel is actually less volatile than regular.
Some automotive engines do in fact require premium. Engines with a compression ration of 10:1 require the higher octane fuel to prevent predetonation (due to the higher pressure levels in the cylinders).
