Amazon.com Inc.’s recent breakup with longtime shipping partner FedEx Corp. shows how far the e-commerce giant has come in creating its own delivery network.

Over the years, Amazon has played down its ambitions. But as consumers flock to its site for everything from toilet paper to TVs, Amazon has quietly blanketed the nation with hundreds of sprawling suburban warehouses and neighborhood package-sorting centers, flooded the streets with tens of thousands of vans and even taken to the airways. The costly effort is enabling...