The Greek god of sleep is most closely associated with Hypnos who was the personification of sleep, but his son Morpheus, also a god of sleep and dreams, is a more familiar name in popular culture. In truth, both Hypnos and Morpheus are gods of sleep.
Hypnos: Greek God of Sleep and Dreams
Hypnos is the son of the Greek goddess Nyx. Nyx is the goddess of the night and darkness. Her son, Hypnos is the god of sleep. Hypnos is said to have fathered three sons known as the Oneiroi: Morpheus, Phobetor and Phantasos. Morpheus, like his father, became closely associated with sleep and dreams. A visit from Morpheus alludes to pleasant, sweet dreams or the dreams of a king, restful and rewarding.
According to Spartan myth, the warlike people associated the god Hypnos closely with his twin brother Thanatos. Thanatos was the Greek god of death. Hypnos governed the "little death"' or the sleep from which you could awake and Thanatos governed the sleep from which you never awake.
Edith Hamilton's mythology details one legend that is closely associated with Hypnos and may be what led to the etymology of the word hypnosis. In the myth, Endymion is a shepherd that deeply admires the night sky and the moon goddess Selene. Selene falls in love with the handsome boy and often watches over him while he sleeps. Selene entreats Zeus to preserve her love. Zeus commands Hypnos to put Endymion into a deep sleep for Selene so that he may remain forever young. It is said that Hypnos obeys Zeus' command, but that he leaves Endymion asleep with his eyes open so he may always look upon the beauty of his love: Selene.
Sleeping with your eyes open is a common phrase associated with hypnosis.
Morpheus: Son of Hypnos
Morpheus and his brothers are portrayed as handsome men with broad wings upon their backs. Some artwork suggests their angelic appearance was an important part of their visitations into and out of dreams. Morpheus guards his realm with two creatures capable of becoming nightmares. Morpheus, along with his brothers Phobetor and Phantasos divided the types of dreams they handled. Phobetor delivered fearful dreams and is the source of the word phobia, while Phantasos brought the fantastical dreams or fantasies. Morpheus delivered dreams to all, but took particular care with the dreams of kings and heroes.
The name for morphine also owes its entomology to Morpheus because of the medication's ability to make people sleepy.
Sleep in Pop Culture
The god of sleep is popular in modern culture, being retrofitted as the Sandman in comic books, commercials and film. In the science fiction, fantasy television program Xena: Warrior Princess, Morpheus makes an appearance as do many other Greek gods. Author Neil Gaiman writes about Morpheus as the principle character in his comic book series: Sandman. In the film trilogy Matrix, Morpheus is the character played by Laurence Fishburne who awakens humans like Keanu Reeves' Neo from their 'dream-like' state in the matrix.
While Hypnos is the personification of sleep, his son Morpheus is most closely associated with the title of Greek god of sleep in modern culture.