According the to Hesiod, the first race of man arose during the reign of Cronus and the Titans. These first humans were not made of flesh, but instead of gold, hence the term 'Golden Age'. The men of the golden age lived a life free from toil, disease and aging. Once gone, this race was followed by races of successively inferior metals.
It was the Romans, whoever, who seem to have created our modern concept of the Golden Age. They translated the Greek word γενός, which means 'race', with saeculum, which means 'age'. To the Romans, the golden age was a time when Saturn ruled the earth, which provided everything for man, and so toil was unnecessary. Because of this abundance, there was no sin and laws were thus unnecessary.
Over time, the world became a less fertile and more hostile environment for man. Man as well devolved along with the earth, becoming smaller and weaker with each generation. Not to mention the introduction of women via Pandora. This decline led to the the successive deterioration of the ages, from Golden to Silver, then Bronze. The Bronze age was an especially militant one, filled with demigods battling each other. To rid the world of this race, Zeus sent a flood down to earth. Only two people survived, Deucalion and Pyrrha (Prometheus' son and Epimetheus' daughter, respectively). From their children arose our own age, the Iron Age.
Hesiod. Works and Days.