In some versions of Greek mythology, Zeus ate his wife Metis because it was known that their second child would be more powerful than him. After Metis's demise, their first child Athena was born when Hephaestus cleaved Zeus's head open and the goddess of war emerged, fully grown and armed.
In order to forestall these consequences, Zeus tricked Metis into turning herself into a fly and promptly swallowed her. However, she was already pregnant with their first and only child, Athena. Metis crafted armor, a spear, and a shield for her daughter, whom she raised in Zeus' mind.
According to a prophecy, Metis would bear two children, the first being Athena, while the second one, a son, would be so powerful that would overthrow Zeus. Zeus, afraid of this, tricked Metis into turning herself into a fly, and swallowed her.
There offspring were the first of the Olympians. To insure his safety Cronus ate each of the children as they were born. This worked until Rhea, unhappy at the loss of her children, tricked Cronus into swallowing a rock, instead of Zeus.
The gods eventually won and overthrew the Titans. Zeus then cut up his father Cronus and threw him into the pit of Tartarus. His Roman equivalent is Saturn.
Lycaon, the king of Arcadia, also offered his son's roasted flesh to Zeus. It was atrocious behavior to serve human flesh to him, as Zeus had a dislike for humans in general.
Athena, the daughter of Zeus, was produced without a mother and emerged full-grown from his forehead. An alternative story was that Zeus swallowed Metis, the goddess of counsel, while she was pregnant with Athena so that Athena finally emerged from Zeus.
A while later, he rapes her, she agrees to marry him and they create a family on Mount Olympus, the Deities' new home. Unfortunately, Zeus constantly cheats on Hera and he has done it over a hundred times, but in the end Hera always forgives him.
Perhaps partly because of the strange circumstances of her birth, Athena is often cited as Zeus's favourite child. He also greatly admired her strength of character and fighting spirit. Some believe Athena was Zeus's first born child, which might, somewhat unfairly, suggest why he chose her as his favourite.
In his private life Zeus was quite the lothario, fathering an unbelievable number of around 100 children with many different women (but don't hate him too much – it's just a myth, after all). Of this 100, he fathered a mix of sons and daughters, many of whom were gods and goddesses, and some became great leaders.
But Rhea, his wife, saved the infant Zeus by substituting a stone wrapped in swaddling clothes for Cronus to swallow and hiding Zeus in a cave on Crete. There he was nursed by the nymph (or female goat) Amalthaea and guarded by the Curetes (young warriors), who clashed their weapons to disguise the baby's cries.
She was affected by the evil's, becoming greedy and ambitious to rule the world after the destruction of the Greek pantheon. She could have been jealous of Zeus' authority over the world, which would also explain why she wanted Kratos to kill him.
Zeus & Cronus
To pre-empt any takeover he, therefore, swallowed all of his children: Hestia, Demeter, Hera, Hades, and Poseidon.
Typhon attempted to overthrow Zeus for the supremacy of the cosmos. The two fought a cataclysmic battle, which Zeus finally won with the aid of his thunderbolts.
Fearing he would be overthrown, Cronus swallowed his newborn children retaining them inside his own body where they could do him no harm. Cronus' wife Rhea saved Zeus by tricking Cronus into thinking a wrapped stone was their newborn. Zeus eventually grew up and defeated his father.
Ganymede (or Ganymedes) was a young man from Troy. His beauty was unparalleled, and for that reason, Zeus abducted and brought him to Olympus to serve as his cupbearer and lover. Ganymede's myth is an important step in queer history, but there is also a dark side to the story.
Io, in Greek mythology, daughter of Inachus (the river god of Argos) and the Oceanid Melia. Under the name of Callithyia, Io was regarded as the first priestess of Hera, the wife of Zeus. Zeus fell in love with her and, to protect her from the wrath of Hera, changed her into a white heifer.
Leto was said to be one of Zeus's consorts. She gave birth to Artemis and Apollo after a good deal of persecution at Hera's hands. Zeus finally became enamored of the goddess who was to become his permanent wife — Hera.
Hermes realized what needed to be done and directed Hephaestus to take a wedge and split open Zeus's skull. Out of the skull sprang Athena, full grown and in a full set of armour. Due to her manor of birth she has dominion over all things of the intellect.
In Percy Jackson book 4, this very question comes up in a conversation between Percy and Annabeth, but for those who can't wait, here's the author's explanation. Athena, as you may know, was not born in the normal way. She sprang from Zeus's head in full battle armor. Her children have similar magic births.
Athena's feelings about Poseidon are not really discussed, though they are clearly rivals. Athena and Poseidon entered into a contest to be the patron of Athens. Poseidon produces a spring of water but it was salty. Athena bested Poseidon by producing an olive tree on the Acropolis.
Moreover, in his quest to test Zeus' immortality Lycaon attempted to murder the god while he slept. Thereupon Zeus brought the roof down and transformed the fleeing Lycaon into a wolf.
When Zeus grew older he wanted to rescue his brothers and sisters. He got a special potion and disguised himself so that Cronus would not recognize him. When Cronus drank the potion, he coughed up his five children. They were Hades, Poseidon, Demeter, Hera, and Hestia.