Lilith, Adam's first wife
The passage in Genesis 1:27 — "So God created man in his own image, in the image of God created he him; male and female created he them" (before describing a mate being made of Adam's rib and being called Eve in Genesis 2:22) is sometimes believed to be an indication that Adam had a wife before Eve.
Also according to midrashic literature, Adam's first wife was not Eve but a woman named Lilith, who was created in the first Genesis account. Only when Lilith rebelled and abandoned Adam did God create Eve, in the second account, as a replacement. In an important 13th century Kabbalah text, the Sefer ha-Zohar ("The Book of Splendour") written by the Spaniard Moses de Leon (c. 1240-1305), it is explained that:
At the same time Jehovah created Adam, he created a woman, Lilith, who like Adam was taken from the earth. She was given to Adam as his wife. But there was a dispute between them about a matter that when it came before the judges had to be discussed behind closed doors. She spoke the unspeakable name of Jehovah and vanished.
In the Alpha Betha of Ben Sira (Alphabetum Siracidis, or Sepher Ben Sira), an anonymous collection of midrashic proverbs probably compiled in the 11th century C.E., it is explained more explicitly that the conflict arose because Adam, as a way of asserting his authority over Lilith, insisted that she lie beneath him during sexual intercourse (23 A-B). Lilith, however, considering herself to be Adam's equal, refused, and after pronouncing the Ineffable Name (i.e. the magic name of God) flew off into the air.
As a side note, this places Lilith in a unique position, for she left the Garden of her own accord and before the Fall of Man, and so is untouched by the Tree of Knowledge. However, to know the true name of God is to have power over him.
Lilith went on to mate with Asmodai and various other demons she found beside the Red Sea, creating countless lilin. Adam, distraught and no doubt also angered by her insolent behaviour, urged God to bring Lilith back. Three angels were dispatched after her, named Senoy, Sansenoy, and Semangelof. They made threats to kill one hundred of Lilith's demonic children for each day she stayed away, but she countered that she would prey eternally upon the descendants of Adam and Eve, who could be saved only by invoking the names of the three angels. She never returned to Adam.