Multiple tests have shown that fuel octane level has no role in mileage and maintenance. Octane level only says something about detonation resistance, the caloric value (amount of energy) in the fuel does not increase with a higher octane level.
It could however infuence the amount of power that an engine can produce. If you have a high-performance engine with a high compression ratio or a big turbocharger, often a high-octane fuel is recommended (or even required) in order to produce the maximum amount of power. This is not an issue in most everyday cars, they will run happily on any fuel that meets the minimum requirements.
To add a quote from wikipedia:
Many high-performance engines are designed to operate with a high maximum compression, and thus demand fuels of higher octane. A common misconception is that power output or fuel efficiency can be improved by burning fuel of higher octane than that specified by the engine manufacturer. The power output of an engine depends in part on the energy density of the fuel being burnt. Fuels of different octane ratings may have similar densities, but because switching to a higher octane fuel does not add more hydrocarbon content or oxygen, the engine cannot develop more power.