The ancient Greek poet Hesiod claims that Hypnos was the son of Nyx (the goddess of Night) in the Theogony. In Hesiod's version, he has no father. However, Hypnos does have a brother - the god of death, Thanatos. Hypnos and Thanatos were often portrayed together in both myth and art, and indeed, the pair cooperated on a number of occasions.
One memorable example of the manner in which the brothers worked together is found in Homer's Iliad. In a poignant scene, Homer describes how the hero Sarpedon, so recently killed in battle, is reverently carried away from the battlefield by Hypnos and Thanatos. This scene in turn inspired the ancient Greek artist Euphronios to paint a magnificent image that represented the gods, complete with wings and armor, gently lifting the lifeless body of Sarpedon.
Hypnos also acted alone in mythology, literature, and poetry. There is a delightful interlude in the Iliad that involves Hypnos, Hera, and Zeus. Hera visits Hypnos, and asks him for a favor - you see, the goddess wants to distract her husband Zeus from the events taking place. So she requests that the god of sleep use his powers on Zeus. However, Hypnos is reluctant to meddle with the ruler of Olympus. Hera then offers Hypnos an irresistible bride as a bribe - Pasithea, one of the younger Graces or Charites. In the end, the god of sleep agrees to cast his spell on Zeus.
It was also believed that Hypnos was the father of the Dreams. This means that he was therefore the god Morpheus's father.
Hypnos was known as Somnus in Roman mythology.
Who's Who in Classical Mythology