To maximize your engine's life, you should change the oil and filter every 3,000 miles. At this point you should also say several quiet prayers to the gods of breakdowns and have a mid-ranking church official -- no lower than a nun but no higher than a bishop -- bless the water in your vehicle's coolant.
The idea that you should change your car's oil every 3,000 miles is so pervasive that it has its own Wikipedia page ... specifically debunking it. This misconception has its roots laid all the way back to the 1970s, when oil technology was still developing and the engine operating environment wasn't nearly as smooth and controlled as it is today. Back then, 3,000 miles was actually a pretty good rule of thumb. So was "Never trust a European" and "Chest hair, son: Always chest hair." However, just like international relations and grooming habits, engine and oil technology have improved drastically over the decades. The life of the oil in your car has now increased far beyond that allegedly sacred 3,000-mile barrier.
So why do we hang onto it? Because no one has bothered to tell the oil-change industry. Those poor, naive fellas still "recommend" changing it every 3,000 miles, despite the fact that synthetic oils lasting up to 15,000 miles have been available for years. If only somebody would show them the backs of those bottles in their tiny, uncomfortable lobbies; why, we're sure they'd immediately mend their ways and return all that needlessly spent money of yours.