The Fates, or Moirai, were the three goddesses of human destiny. They were represented by three spinning crones: Clotho, who spun the thread of life; Lachesis, representing chance, who measured it; and Atropos, the inevitable, who cut it.
The Furies, also known as the Erinyes or Eumenides, were the three hideous goddesses of vengeance, conceived from the drops of blood spilt when Chronos castrated his father Uranus2. Alecto, Megaera, and Tisiphone had snakes for hair, had wings on their backs and lived in the underworld.
The Graeae were three old hags, sisters of the Gorgons, whose cave the hero Perseus had to visit in order to find the whereabouts of Medusa. They were blind and toothless except for one eyeball and one tooth which they passed between one other.
The Graces, on the other hand, were daughters of Zeus who personified beauty, charm and joy. Euphrosyne, Aglaea and Thalia have been famously represented in oils by Raphael and in marble by Canova. One version of the famous sculpture 'graces' London's Victoria and Albert Museum.
The Sirens were three sea nymphs, Parthenope, Ligeia, and Leucosia, daughters of Calliope, who seduced passing seamen with their singing, so that they stopped sailing, became shipwrecked on their rocky island and eventually died of hunger. After Odysseus, having been tipped off by Circe, defied them by having himself tied to the mast, having plugged his fellow sailors' ears with wax. The Sirens consequently threw themselves to their deaths.