According to Greek mythology Cancer was the crab sent by Hera to distract Hercules as he fought the Hydra in the marshes at Lerna.  Hercules trod on it during the course of the long battle, whence Hera placed it amongst the stars for it's service.

Alpha (a) Cancri is also known as Acubens, which means claw.  It marks one of the large front claws that are common on crabs; the opposite claw is marked by iota Cancri but it has no other name.

Gamma (g) and delta (d) Cancri are known as Asellus borealis and Asellus australis respectively.  Their names mean the Northern Donkey and the Southern Donkey, and they are eating from the large open star cluster called Praesaepe, which means "the Manger."  Some stories say they are the donkeys in the stable when Jesus was born, other stories say they were two donkey's that helped the Titans during the war with Zeus and his siblings in Greek mythology.  Praesaepe is little used now, the common name of the Beehive is becoming popular instead.  If one looks carefully through large binoculars or a small telescope you may be able to make out the pyramid-like beehive with a few bees buzzing around it.