Perhaps partly because of the strange circumstances of her birth,
1. Apollo: Zeus' Best-Known Son. Of all the sons Zeus fathered, Apollo is perhaps the best known. Apollo was conceived during an illicit affair between Zeus and Leto (Zeus was married to Hera at the time), along with a twin sister named Artemis.
Zeus finally became enamored of the goddess who was to become his permanent wife — Hera. After courting her unsuccessfully he changed himself into a disheveled cuckoo. When Hera took pity on the bird and held it to her breast, Zeus resumed his true form and ravished her.
Heracles – Son of Zeus and Alcmene
He possessed superhuman strength and courage. Because he was a reminder of Zeus's unfaithfulness, Hera made it her mission to make his life miserable. At one point, she drove him to madness and he killed his own children. To atone for his sins, he went through his famous “Labors”.
Zeus'favourite son is Heracles, & his favourite daughter is Athena.
Hebe was the youngest daughter to Zeus and his wife Hera. Her name came from the Greek word for 'youth', and it was thought she had the power to temporarily restore youth in a chosen few.
Hera. The most famous of Zeus' wives, Hera was also the sister of the father of the gods, and the goddess of women, marriage, family, and childbirth.
Generally, Zeus is believed to have had over 100 children, but the number could be even greater considering the number of concubines that he had.
But even that trusted source doesn't have them all. In total, Zeus is believed to have fathered more than 50 children! That's not unheard of in ancient Greek mythology.
However, Zeus was afraid of Nyx, the goddess of night.
Nyx is older and more powerful than Zeus. Not much is known about Nyx. In the most famous myth featuring Nyx, Zeus is too afraid to enter Nyx's cave for fear of angering her.
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 the history of homosexuality.
Suffice it to say that Zeus was constantly involved in extramarital affairs. Throughout the various and sometimes contradictory myths composed by Greek authors, there are at least 20 divine figures with whom he consorted, and about twice as many mortals.
The Titan goddess Leto had been one of Zeus' lovers even before he married Hera. However, when Leto became pregnant with Zeus' twins Artemis and Apollo, Hera and Zeus were already married. This understandably made Hera extremely jealous.
Once the festivities came to an end, Zeus and Hera had a glorious wedding night that lasted a staggering 300 years. Together, the two love birds had three children: Ares the god of war, Eileithyia, the goddess of childbirth and Hebe, the goddess of youth.
Hermes has many children and all undetermined children go to Cabin 11 as explained by Luke in The Lightning Thief. His favourite child is Luke Castellan, who he loved so much to the point he became his pride and joy, according to Poseidon told Percy in The Titan's Curse.
What is this? Athena, Zeus's first born and favorite child, is the Goddess of Wisdom. According to her origin story, Athena sprang from Zeus's head, fully-grown, after he swallowed his first wife, the Titan Metis, who was pregnant with Athena at the time.
Impregnation by Zeus
Nonnus classifies Zeus's affair with Semele as one in a set of twelve, the other eleven women on whom he begot children being Io, Europa, Plouto, Danaë, Aigina, Antiope, Leda, Dia, Alcmene, Laodameia, the mother of Sarpedon, and Olympias.
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.
Castor and Pollux (the Dioscuri) are figures from Greek and Roman mythology considered the twin sons of Zeus or Jupiter. Semi-divine figures, they were credited with the role of saving those in trouble at sea or in grave danger in war and were particularly associated with horses and sports.
Before his marriage to Hera, Zeus consorted with a number of the female Titanes (and his sister Demeter). These liaisons are ordered by Hesiod as follows: (1) Metis; (2) Themis; (3) Eurynome; (4) Demeter; (5) Mnemosyne; (6) Leto.
Why is Zeus married to his sister? To hide her shame, Hera agreed to marry him. It was a violent marriage at best. Though Zeus had pursued his sister and sought to possess her by marriage, he never gave up his lusty ways.
Metis, an Oceanid or sea-nymph, was Zeus's first wife. Wise and prudent, she was endowed with the gift of prophecy. In their early years together, she was Zeus's closest ally and aide, helping him win the battle against Cronus.
II.
Aphrodite later and of her own volition had an affair with Zeus, but his jealous wife Hera laid her hands upon the belly of the goddess and cursed their offspring with malformity. Their child was the ugly god Priapos.
Zeus fell in love with Io and seduced her. To try to keep Hera from noticing he covered the world with a thick blanket of clouds. This backfired, arousing Hera's suspicions. She came down from Mount Olympus and begain dispersing the clouds.
Hera was worshipped throughout the Greek world and played an important part in Greek literature, appearing most frequently as the jealous and rancorous wife of Zeus and pursuing with vindictive hatred the heroines who were beloved by him.