Egyptian
The early Egyptians saw this area in the sky as a scarab, or a dung beetle. It was representative of their goddess of the dawn, Khephri, and was an icon of fertility.
Greek
To appreciate the significance of the Greek mythology behind Cancer, you must know the story of Hercules (Heracles in Greek). The powerful head of the gods, Zeus, had an affair with a mortal woman, which resulted in the birth of Hercules, who was despised by Zeus's wife, Hera.
Second Labor
In a fit of madness sent by Hera, Hercules killed his wife and children. To find redemption he had to perform 12 Labors. In the second labor he faced the Hydra---a hundred--headed monster.
Giant Crab
Hera sent a giant crab to distract Hercules while the hero battled the Hydra. The crab grabbed Hercules by the heel, but Hercules crushed it with his foot, killing it.
Constellation
To reward its service, Hera placed the crab in the heavens as a constellation, according to the Greek myth. Nevertheless, since it had failed in its duties, she refused to give it any bright stars to mark its position in the sky.