In The Iliad, the Greeks' best fighter, Achilles, gets angry at the leader of the Greek army, Agamemnon, for ransoming one of his concubines back to the Trojans.
The first consequence of Achilles' anger is that he retaliates against Agamemnon and the Greeks by refusing to fight. Achilles even pulls his soldiers, the intrepid Myrmidons, off the field.
The second consequence of Achilles' anger is that his refusal to fight swings the tide of the war. Up until this point, the Greeks had laid siege to the city of Troy for 10 years. While the siege had become a stalemate, the fact remained that the Greeks had the city surrounded, leaving the Trojans powerless to do anything but merely survive inside the city's walls. Without Achilles and the strength of his Myrmidons, the Trojans, led by the heroism of Hector, go on the attack and push the Greeks all the way back to their ships.
The third consequence of Achilles' anger is the death of his beloved friend, Patroclus. With the Trojans about to push the Greeks into the sea and defeat near, Patroclus begs Achilles to accept Agamemnon's apology and fight. Achilles refuses but lets Patroclus don his armor and rush into battle with the Myrmidons at his side. The other Greek soldiers, thinking that Achilles had taken the field again, push back the Trojan advance. However, Patroclus gets killed by Hector, making Achilles swear vengeance against Hector.