If regular (87 octane) gas is used in a car that recommends premium gas, can the engine be damaged. I've read that the horespower can be slightly diminished and I've also read that the gas miliage can be affected as well, but I haven't read anything about damage to the engine. Thanks.
Yes. Octane is a chemical that is added to gas to make it less explosive. The reason for this when the piston inside of your engine compresses the fuel air mixture, it can explode before the spark plug fires. If this happens, the piston will fire down the cylinder wall before the crank shaft and the piston rod reach their piviot points. If this happens you will hear a " ping" or a " spark knock". This (in time) will destroy an engine.
The higher the octane rating the less explosive the fuel and the higher the compression can be in the engine - thus more horse power. The lower is just the opposite.