The Trojan War provides the background for much of both Greek and Roman literature. When Paris handed Aphrodite the prize, the apple of discord, he started the series of events that led to the destruction of his homeland Troy, which, in turn, led to the flight of Aeneas and the founding of Troy. On the Greek side, the Trojan War led to the murder of his daughter Electra by Agamemnon, his own murder at the hands of his wife, Clytemnestra (Helen of Troy's sister), and her murder at the hands of her son.
Unravel these twisted threads with the articles on the Trojan War.
Sometimes called Ulysses, Odysseus was the most famous hero of the Trojan War who made it home. Granted, the war took ten years and his return trip another ten, but he made it back safely to a family that was, oddly, still waiting for him. His story makes up the second of the two works attributed to Homer,
The Odyssey, which contains more fanciful encounters with mythological characters than
The Iliad.
The House of Atreus was cursed. Horrible crimes were committed by the members of this house, which included Agamemnon and Orestes. In the Greek dramatic festivals the tragedies frequently centered on one or another member of this royal house.
Another famous house that couldn't keep from violating major societal laws was the Theban royal house of which Oedipus, Cadmus, and Europa were important members who featured prominently in tragedy and legend.
Hercules was immensely popular and continues to be. His behavior was not always admirable but Hercules (Heracles or Herakles) paid the price without complaint, defeating impossible odds, time and again. Hercules also rid the world of horrible evils. All his tastes were superhuman, as befits the half-mortal son of the god Zeus. Herodotus finds a Hercules figure in Egypt.
Fruits play important roles in Greek mythology. The apple, familiar from the story of the Garden of Eden, was used in Greek mythology (and in real life) as a means of gaining one's end.
A collection of legends and retellings of the Greek myths. There are also public domain texts of the Greek myths told by Nathaniel Hawthorne and Thomas Bulfinch.