The Odyssey / O Brother Where Art Thou

The Odyssey: Main character is Odysseus (Latin name Ulysses)
O Brother: Main character Everett's full name is Ulysses Everett McGill

The Odyssey: Ulysses is trying to get back home to his wife Penelope on the Island of Ithaca
O Brother: Everett is trying to get back home to his wife Penny in Ithaca, MS

The Odyssey: Tiresias is a blind seer that Odysseus encounters in the underworld
O Brother: Everett meets a blind seer at the beginning of the movie

The Odyssey: Poseidon has a personal vendetta against Ulysses and pursues him the entire narrative, constantly hampering his journey home
O Brother: Sheriff Cooley similarly pursues the three men for the entire film

The Odyssey: Penelope has 108 young men collectively called The Suitors who are vying for her hand
O Brother: Penny has Vernon T. Waldrip, and Everitt's daughter repeatedly claims "He's a Suitor."

The Odyssey: Homer is known as the blind poet / blind bard

O Brother: The man working the radio station (a modern day bard in a way) is blind

The Odyssey: The siren's song entrances men and lures them to their doom
O Brother: The men are completely entranced by the laundry ladies' song.

The Odyssey: Odysseus's men behave like pigs in the house of the witch-goddess Circe, so she gives them drugged wine and turns them into swine

O Brother: The laundry ladies are also tied to Circe. They give the men drugged alcohol, and Pete gets "turned into" a horny toad

The Odyssey: The cyclopes Polyphemus attacks Odysseus's men after they eat the food in his cave

O Brother: One-eyed Big Dan attacks the men as they are feasting

The Odyssey: The cyclops kills Odysseus's men by picking them up, crushing them, and bashing them against the rocks

O Brother: Big Dan kills one of Everett's "men" by picking him up, crushing him, and bashing him against a tree

The Odyssey: The cyclopes is blinded by a wooden stake that has been burned in fire

O Brother: Big Dan is nearly blinded by a wooden stake, then killed by a wooden cross that has been burned in fire

The Odyssey: Odysseus and his men escape the cyclops dressed as white sheep

O Brother: Ulysses and his men escape Big Dan dressed in white sheets. Could also take it as the KKK being "sheep" who of course are white.

In The Odyssey, Odysseus's men kill the sacred cows of Helios, and Zeus punishes them with thunderbolts. In O Brother, Where Art Thou? (2000), "Baby Face" George Nelson hates cows and kills them indiscriminately. He is later killed by the electric chair.

The Odyssey: Odysseus's men are told not to kill the sacred cows of Helios. They do anyways, and Zeus punishes them with thunderbolts.

O Brother: "Baby Face" George Nelson hates cows and kills them indiscriminately. He is later killed by the electric chair.

The Odyssey: Menelaus is a character in the Odyssey
O Brother: The "Pappy" in Gov. Pappy O'Daniel's name is a nickname. The character's real name is Menelaus O'Daniel (narratively, he is more in line with Zeus than Menelaus).

The Odyssey: Odysseus attends a feast disguised as an old beggar, after which the Suitors exit the story (he kills them)

O Brother: Everett attends a dinner disguised with an old man's beard, after which the Suitor exits the story (political campaign over)

The Odyssey: Zeus causes a shipwreck, and Odysseus escapes drowning in rushing waters by clinging to wood (fig tree)

O Brother: Everett escapes drowning in rushing waters by clinging to wood (coffin)

The Odyssey: Odysseus's name may be a play on the Greek verb odussomai (to suffer pain), "the man of pain". Other sources call him a "man of suffering". He's very much a man of "constant sorrow."

O Brother: /r/NoisyImages/