Hestia Greek goddess of the hearth was the daughter of the Titan Cronus and Titaness Rhea. She was the first born of their children and, as such, the first of the Olympians. Her siblings were Demetra, Hera, Hades, Poseidon, and Zeus. Her Roman counterpart was called Vesta.
But Cronus had this bad habit of swallowing his children, so she was the first to be swallowed! When Zeus, the last born, forced his father to disgorge his brothers and sisters, she was the last one to reappear. That's why it can be said that she was the first and also the last of Cronus and Rhea's children.
Both Poseidon and Apollo wanted to marry her, but Hestia the Greek goddess did not like the works of Aphrodite, so she swore on the head of Zeus (i.e. really touching Zeus' head) to remain a virgin forever.
Instead of marriage, Zeus decided to give her the honour of being worshipped in all the houses and temples, in fact the family hearth in every house was her altar (the very name Hestia means "hearth" in Greek). Also in the temples there was a place for the her hearth. The fire in the households and temples had to be kept burning at all times.
Each city and village had its sacred fire, kept in a building called Prytaneum. This was the building where the foreign guests and ambassadors were received. A flame of this fire was taken to the new colonies and it symbolized the connection between the new colony and the metropolis.
Hestia was said to have invented the art of building houses, that's why she was given powers over the altars and shrines and the first prayers and the first share of the sacrifices were offered to her (the first, and also the last). There was also an expression "Hestia comes first" and Plato, in describing how an ideal city should be build, specified that a sacred area had to be set apart for Hestia, Zeus and Athena.
There are no specific stories about Hestia Greek goddess of the hearth. While all the other gods roamed around and had all kind of adventures, Hestia remained on mount Olympus and guarded the sacred fire. She reigned over the security of the home and she was a protector of those who were seeking asylum at the hearth of a house or of the Prytaneum.
Hestia Greek goddess of the hearth was a kind hearted and peaceful deity. She did not like to take part in the the other gods' struggles and she just gave up her position as one of the twelve olympians and left Dionysus in her place.