The Myth, the Legend
Dating back to 1400 BC, the Oracle of Delphi was the most important shrine in all Greece, and in theory all Greeks respected its independence. Built around a sacred spring, Delphi was considered to be the omphalos - the center (literally navel) of the world.
People came from all over Greece and beyond to have their questions about the future answered by the Pythia, the priestess of Apollo. And her answers, usually cryptic, could determine the course of everything from when a farmer planted his seedlings, to when an empire declared war.
Arguments over the correct interpretation of an oracle were common, but the oracle was always happy to give another prophecy if more gold was provided. A good example is the famous incident before the Battle of Salamis when the Pythia first predicted doom and later predicted that a 'wooden wall' (interpreted by the Athenians to mean their ships) would save them.
The lack of a strict religious dogma associated with the worship of Greek gods also encouraged scholars to congregate at Delphi, and it became a focal point for intellectual enquiry, as well as an occasional meeting place where rivals could negotiate.
Delphi became a fantastic showcase of art treasures and all Greek states would send rich gifts to keep the Oracle on their side. It finally came to an end in the 4th century AD when a newly Christian Rome proscribed its prophesying.