Like the Giants, the Titans (Greek Tιταν, plural Tιτανες) are potencies belonging to an early pre-Olympian stage of Greek mythology. The Giants and the Titans tend to be confused with each other, but in origin they are distinct.
The genealogy of the gods given in Hesiod's Theogony names twelve Titans as children of Uranus, the sky, and Gaia, the Earth:
Other Titan offspring named in mythology are:
Hecatonchires, who each had fifty heads and a hundred hands, and the three Cyclopes, who each had a single eye. After these came the twelve Titans. However, Uranus considered his early offspring monstrous, and imprisoned the Hecantochires and the Cyclopes. Furious, Gaia made overtures to the Titans to overthrow Uranus, to which only Cronus (the youngest) would listen. He lay in wait for his father with a sickle, and castrating him, took his place as ruler of the universe. Cronus had the help of the Hecatonchires and the Cyclopes, since he freed them from their imprisonment in Tartarus. After Uranus was deposed, however, Cronus returned the Hecatonchires and Cyclopes to Tartarus.
From the blood of Uranus, Gaia later brought forth the Gigantes, who were destroyed by the gods with the help of Heracles. His genitals also turned into the goddess of beauty, Aphrodite.
Cronus took over the crown of the world and the heavens and married his sister Rhea
Cronus had the habit of swallowing his own children right after their birth because his mother, Gaia had prophesied that one would eventually depose him as ruler of the universe in the same manner Cronus had taken over, by overthrowing his father. The last child was Zeus, whom Rhea protected by giving Cronus a stone wrapped in a baby's cloth to swallow.
Rhea hid the infant Zeus in a cave on Mount Ida in Crete. According to one version of the story, he was then raised by a goat named Amalthea. Koryvandes, a company of soldiers (or smaller gods) danced, shouted and clapped their hands to make noise so that Cronus would not hear the baby's cry. It was sometimes also said that he was nursed by a nymph named Adamanthea. Since Cronus ruled over the earth, the heavens and the sea, she hid him by dangling him on a rope from a tree so he was suspended between earth, sea and sky and thus, invisible to his father.
When he grew up, Zeus revolted against his father's tyranny. He won this war, the Battle of Titans, and set his brothers and sisters free by cutting his father's stomach open. He also rescued the Hecatonchires, Gigantes and Cyclopes from Tartarus; they helped him overthrow the Titans. The Cyclopes fashioned the lightning bolts Zeus was famous for. He shared the world with his elder brothers, Poseidon and Plouton (or Hades) after drawing lots: Zeus got the land, Poseidon the sea and Plouton the world of the shadows (the dead).
There is another Titan myth which appears as early as Onomacritos. In this version of the story, according to classic scholar Jane Ellen Harrison, the Titans lure away the infant Zagreus, dismember him, cook and eat him. Says, Harrison:
"The story is an initiation myth based on the familiar initiation ritual of the mock death and resurrection of the initiate. The initiators are the elders or dynasts of the tribe, the embryo-kings. The Titans as old-world kings are well in place; as a form of giant they are absurd. The name Zagreus takes us to Crete, and in Crete we find the Titans in a connexion that again points to initiation mysteries. The Cretans, according to Diodorus, said that in the time of the Kouretes those who were called Titans ruled over the region of Cnossos, where were shown the foundations of the house of Rhea and a sacred cypress-grove of hoary antiquity. These Titans again must have been the old king-medicine-men, contemporary with the Kouretes and, like them, initiators into the men's house of the Mother Rhea. On a red-figured hydria in the British Museum Zagreus is depicted as actually devoured by the Titans, and these Titans wear the characteristic dress of Thracian chieftains. We may safely infer that the Titan myth of the rendering of Zagreus was known from Thrace to Crete, and we may suggest that it arose in the early stratum of satem-speaking population known to the later Greeks as Pelasgian -- a stratum specially addicted to the mystery-cults of the son of Semele." Source of quote: Encyclopedia of Religion and Ethics, 1908-1926, ed. by James Hastings.
Various large things were named after the Titans, for example the RMS Titanic; see also Titan.