Should you use premium unleaded instead of regular unleaded for your 2004 V-6 Ford Mustang?

No, the V6 Mustang was designed to run on Regular Unleaded. Using Premium fuel is of no benefit whatsoever. Higher octane fuel does not provide more energy, more power, better mileage, more torque, burn cleaner, and is not better for the environment. In fact your engine may very well perform worse on a high octane fuel. High performance engines are designed to run on high octane fuels due to their high compression. Your V6 is not a high compression engine and you cannot make your engine a race engine just by upping the octane. Save your hard earned money, and use exactly the octane you need. Using a Higher Octane is a waste of money unless you have a car that requires it.