It all depends on the car. Read the owner's manual to find out what you should use.
If the manual specifies premium only, don't use anything less. (In an emergency, you can put in a little bit of regular just to get to the nearest station that sells premium.)
If the manual recommends premium, but says you can use regular, too, you will find that performance, including gas mileage, is better with premium. It may be enough to wipe out the price difference between premium and regular.
If the manual specifies regular, using premium won't do any harm, but the car won't perform any better on it than it does on regular. Here, using premium is completely a waste of money.