The nymph Calypso begged Odysseus to stay with her.
Elpenor the youngest of Odysseus crew who had fallen off Circe's roof and died, remaining unburied.
Odysseus regales Aeolus with stories of the war at Troy for a month, before leaving. When he returns, Odysseus begs Aeolus for more help, but he is denied.
Odysseus begs for food for many reasons:To get food.To make his disguise more convincing.To test the characters of the suitors.
He wants Odysseus to be her lover and stay with her forever.
In book 7 The King and Queen notice Odysseus. Odysseus begs at his knees, begging for mercy at the Queen. The King and Queen give him a day off and make Odyessuestravel in the Phaeacian ship.
Calypso wants Odysseus to stay with her on the island forever.
Antinous never wants to kill Odysseus, because he never realizes Odysseus is still alive. He may have wanted to kill the beggar, whom is Odysseus in disguise, but is prevented from doing so by honour and Telemachus' threats. Odysseus as a beggar begs from Antinous and curses him when Antinous refuses impolitely. He does want to marry Penelope, Odysseus' wife.
Phemius, son of Terpes is the gifted bard in the Odyssey. He plays for the suitors unwillingly while they feast in Odysseus' palace. When Odysseus fights the suitors, Phemius begs for his life and is spared with Telemachus' intervention.
Because Odysseus loved his wife Penelope too much to stay.
The second lie Odysseus tells the Cyclops is that his ship was wrecked on the rocks of his island due to the wrath of Poseidon, the god of earthquakes. He claims they are the only survivors and begs the Cyclops for help.
Calypso offers Odysseus immortality and eternal youth if he would stay with her forever.
She thinks Odysseus will forget about his home and family and stay with her.