Seers

Herodotus shows this constantly throughout the Histories:  Both Greeks and Persians were deeply reliant on seers (manteis) and omens before major decisions, especially military ones.

Xerxes regularly consults Magi (the Persian priestly caste who served as seers) and pays attention to dreams and portents. Before crossing the Hellespont, there are elaborate rituals and divination. The Greeks are even more conspicuous about it - Spartan kings like Leonidas and later Pausanias, accompanied by seers, and they won't move armies without favorable sacrifices.

A striking example: at Plataea, the Spartans under Pausanias endure Persian arrow volleys while waiting for favorable omens from sacrifice. Men are dying around them, but they won't advance until the seer Tisamenus declares the signs are good. Only then do they attack.

The Athenians, too, consult Delphi about the Persian invasion, and the oracle's ambiguous prophecies about "wooden walls" become crucial to their strategy. The Seven against Thebes were led by the seer Amphiaraus (pic), who foresaw the death of all of them. 

What's interesting is that Herodotus presents this as universal behavior - not peculiarly Greek or Persian. Croesus consults oracles, the Egyptians have their own forms of divination, and the Scythians use willow rods. For Herodotus' world, the divine constantly intervenes in human affairs, and ignoring signs or seers leads to disaster. Those who disregard prophecies (like Croesus's misunderstanding of Delphi) pay dearly.

The Hebrews had the urim and tumim, but I am unsure what they were. I'll ask Claude.