David and Haf are correct. This is commonly misunderstood. Many think "higher octane means better gas, and better for your engine, too". Not true.
IF
the engine is designed to run optimally on regular (and most non-high-performance engines ARE),
THEN
putting mid-grade or premium or racing fuel or octane boosters, etc is a waste of money and usually results in less MPG, not more. And it will NOT increase performance.
Only if the engine is designed to operate on Premium should you bother to actually USE premium. And in that case, you'd better use it! Engine damage can (and often does) occur. Engines designed this way state "Premium Unleaded Only."
Newer engines may state "Premium Unleaded Recommended." Like David said, the engines stating "Premium Unleaded Recommended" are case-by-case studies. Premium fuel WILL likely improve performance. It may also improve MPG. And it may be worth the difference in cost per mile (or the extra boost in performance may be worth any extra cost per mile) for the Premium. You have to do your own comparison with these engines. It's good to have choices, in this case.
