Octane 101 December 17 2013

We've seen people put 87 octane gas in their premium-fuel-only $70,000 car to save a buck. We've seen people pour octane booster into their car that only calls for 87 octane. What are the facts about octane? Is it safe to save a couple of bucks by switching to a octane level lower than the factory recommended level? Do you get more power out of higher octane gas?