With a lower octane fuel the vehicle will be sluggish and with a higher octane than recommended it shouldn't harm the engine. In fact you may notice improved engine performance.

If you put in too high an octane, not much will happen. MAYBE, the ECU will advance the ignition timing and give you a slight performance boost. In general, high-octane fuel by itself does not make power; it merely allows the engine to make power without blowing itself up. Too low an octane will get you into trouble. If it's slightly too low, you will lose a little performance and get a "ping" under acceleration or when climbing hills. This is normal for most vehicles, though I never allow this to happen to my cars. If it's a bit lower, this little ping will turn into the engine slowly getting damaged, especially if you have a high-compression engine, and/or you run forced induction (turbocharger or supercharger). There's a reason that these engines say, "Premium Fuel Only". Story time; Due to age, engine deposits, and tuningm my old Toyota required 91+ octane, but after I gave the car to my father-in-law, he ran 87-octane only. Three months later, the repeated detonations had gradually caused various parts of the bottom end to break. He still drove it, oblivious that anything was wrong even though you could hear the rods knocking two blocks away. To his surprise, it blew less than a week later. It wasn't until afterwards I found out he ignored my warning. If you have one of the older Mazda Wankel engines, kiss the engine good bye. By the time you recognize what the pinging noise is, it's too late; your apex seals are gone. Now, if you have an older car, you MAY be able to retard the timing and run the lower-octane fuel ping-free. SOME newer cars have an ECU that is adaptive enough to do the same thing. However, this is not ALWAYS true, and if you have a high-performance engine, it usually WON'T be; you have to get the good stuff.