In classical Greece, the preeminent oracle was the one at the temple of Apollo in Delphi. This oracle exerted considerable influence across the country, and was consulted before all major undertakings -- wars, the founding of colonies, and so forth. She also was respected by the semi-Hellenic countries around the Greek world, such as Macedonia, Lydia, Caria, and even Egypt. Croesus of Lydia consulted Delphi before attacking Persia, and according to Herodotus received the answer "if you do, you will destroy a great empire." Croesus found the response favorable and attacked, and was utterly overthrown.
The oracle is also said to have proclaimed Socrates the wisest man in Greece, to which Socrates said that if so, this was because he alone was aware of his own ignorance. In the 3rd century A.D., the oracle (perhaps bribed) declared that the god would no longer speak there.
Dodona was the second most important oracle in ancient Greece, dedicated to Zeus, Heracles and Dione.
Another oracle of note lay in Egypt, in a temple dedicated to Ammon, whom the Greeks associated with Zeus. Alexander the Great had visited it, and though what he asked it is unknown, it is certain the oracle hailed him as Ammon's son, which influenced his conceptions of his own divinity.
On Crete lay another important oracle, to Apollo. It was considered one of the most accurate oracles in Greece.
In Norse mythology, the severed head of the god Mimir was taken by Odin to Asgard for consultation as an oracle.
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