Eurynome was easily the most important Goddess of Pelasgian myth. She was the Great Goddess, Mother, Creatrix, Ruler, called the Goddess of All Things.
Eurynome was born from Chaos, and her first work was to separate the water from the sky. When she had accomplished this, she began to dance across the water. It was a beautiful, sensual dance of creation. As she danced, she danced South, and faster and faster she danced until a wind grew behind her. Eurynome caught this new thing, this wind, between her hands and rubbed it into a snake. The snake, called Ophion, watched as the Goddess danced and danced to keep herself warm. He saw Eurynome dancing across the waves and was filled with lust. He coiled his body around the Goddess seven times and made love to her as she danced.
Impregnated by Ophion, soon the Goddess lay the Universal Egg. Ophion wrapped his body around it seven times at Eurynome's bidding. As it opened, the earth spilled forth, born populated with animals and plants.
At this point the Mother ascended to Mt. Olympus and began to watch her children take shape. When she ascended, the serpent Ophion followed her as the Goddess's consort. Eurynome had no problem with this, but when Ophion began to swagger and boast that he alone was responsible for the creation of the world, Eurynome kicked all his teeth out as she threw his butt out of heaven.
The next thing Eurynome did was very interesting, and involves other mythology you might know about. She created the Seven Planetary Powers, putting a Titaness and a Titan over each. Theia and Hyperion were given the Sun and the power of illumination; Phoebe and Atlas were given the Moon and the power of enchantment; Dione and Crius were given the planet Mars and the power of growth; Metis and Coeus were given the planet Mercury and the power of wisdom; Themis and Eurymedon were given the planet Jupiter and the power of law; Tethys and Oceanus were given the planet Venus and the power of love; and Rhea and Cronus took the planet Saturn with the power of peace. If you look at each of the assignments, you'll find they match perfectly.
The first person was a different story. In this tradition, the first human was the man Pelasgus who sprang from the soil of Arcadia (soon followed by others). They made little huts and ate acorns and wore pig-skin tunics. That's all the STORY about her, but now for the explanations.
These myths are ancient ancient myths if they are even real. Back then, according to the theory of a matriarchal prehistory, there were no Gods or priests, only one mother Goddess and her priestesses. Part of the reason for this was that fatherhood was not clearly understood. People believed that women could be impregnated by the wind (like in the story) or eating something funny. Obviously, inheritance was matrilineal. Eurynome was only one of the Goddess's names. Eurynome, "wide wandering," refers to her as the moon traveling across the sky, by the Sumerians she was called the "exalted dove," or, Iahu. The Eurynome cult spread all over the Mediterranean and was really a base for most of the religions of the area.
In the Titan cults that preceeded the Olympic cults (Classical mythology), Eurynome was the daughter of Oceanus the Titan. She was a Titaness married to the Titan Ophion. But in this version, though Eurynome still ruled heaven, Ophion ruled as an equal. The two ruled together on Mt. Olympus until Cronos replaced Ophion and Rhea replaced Eurynome.
By the time Classical mythology came around, Eurynome had shrunk to being one of Zeus' many loves (mother of the Charites) and a gentle Oceanid. A far cry from the All-Powerful Creatrix she was once worshipped as.
Most everything I know about Eurynome came from Robert Graves' The Greek Myths. As a source, he's a little ... creative. And I wouldn't say that this story was necessarily a strictly or correct retelling of a common Greek story, but either way, it's an awesome story!