My 11 cents worth (that's the price difference in my area!):
BMW designs engines to squeeze out every last hp that is reasonable. To do that, as others have said, they choose a higher compression ratio, more advanced timing (increases horsepower), and THEREFORE the higher octane requirement to prevent preignition.
Next, BMW (and all other car manufacturers) put the knock sensor in so they can detect preignition (which WILL damage the engine, this cannot be disputed) and let the computer back off the timing, eliminating the preignition thereby protecting the engine.
So the fact does remain that Premium will give you the best POTENTIAL performance especially under heavy load. But how much performance will you loose using mid-grade? Probably just a few hp, which you really can't feel. As Krafty mentioned, Europe is hit and miss for Premium. In Germany & Austria I had no problem getting Premium. In Italy it did not exist.
But I have and will continue to use Premium because that's what the engine was DESIGNED for. Big Daddy said it best - if I don't run the recommended gas, then I may as well use straight 30 weight oil, no antifreeze, Pep Boys tires, run it thru the carwash, ah, hell just don't even wash it! Well crap, I shoulda bought a Kia!! I am such a dumb ass for buying a BMW!!
By the way, I CAN tell a difference in power and gas mileage when I tow my boat with my Suburban - I getter BETTER gas mileage and can tow faster UP HILLS when I run Premium. That's a fact, jack. I have checked the gas mileage several times using both ratings on the exact same trip. I get about 1 mpg more on Premium.