This is one of the very few Greek beliefs that can be tested against physical evidence, and it half survives the test.
The story is that the dead must pay Charon a fare to be ferried across the water into the underworld, and that a coin was placed in the mouth of the corpse for the purpose — usually an obol, a small silver coin worth a sixth of a drachma, roughly a labourer's fraction of a day's pay. Excavated Greek and Roman graves do contain coins, sometimes in the mouth of the skeleton, sometimes on the eyes, in the hand, or loose in the grave. The practice is real. It is also far from universal: across most Greek cemeteries only a minority of burials contain a coin at all, and the custom appears strongly from around the fifth century BCE and varies enormously by region and period. So the "Charon's obol" is neither a myth without practice nor a rule everyone followed.
He is not in Homer
The Odyssey's underworld has no ferryman, no fare and no boat. Odysseus reaches the dead by sailing to the edge of Ocean and digging a pit. Charon's earliest appearances are in the lost epic Minyas, quoted by Pausanias, and in the painting of the underworld that Polygnotos made at Delphi, which Pausanias describes at length — an old man with a boat, and beside him a man who had mistreated his father being throttled.
By the fifth century BCE he is fully established. Aristophanes' Frogs puts Dionysus in his boat, rowing while a chorus of frogs sings, and the fare is quoted as two obols — a joke about wartime Athenian jury pay. The white-ground lekythoi, oil flasks made specifically for graves, show him constantly: a bearded man in a short workman's tunic and conical cap, standing in the stern with a pole, while Hermes leads a small figure of the dead down to the bank.
That is what he looks like in Greek art. Not a skeleton, not a hooded reaper — a working boatman, shabby and impatient.
Virgil's version, and the hundred years
The Roman treatment is grander and darker. In Aeneid 6 he is terribili squalore, appallingly filthy, with matted white beard, flame-coloured eyes and a cloak knotted at the shoulder, poling a rusty boat, old but with the raw green vigour of a god. The crowd on the bank stretches out its hands; he takes some and pushes others away.
The rule Virgil states is the one that stuck: the unburied cannot cross. They must wander the bank for a hundred years and only then be allowed over. Aeneas meets his own helmsman Palinurus there, lost overboard and washed up unburied on the Italian shore, and can only promise him a tomb. Greek sources are less specific about the term — the deep anxiety about proper burial is thoroughly Greek, and drives the plots of both Antigone and the last book of the Iliad, but the hundred-year sentence is Virgil's formulation.
He is also the being who must be intimidated rather than persuaded: the Sibyl silences him by showing the golden bough, and in later accounts he was punished with a year in chains for ferrying Heracles across without authorisation.
Charun, who is a different creature
Etruscan funerary art has a demon called Charun — the name is close enough that ancient and modern writers have connected them, and different enough that the relationship is disputed. He is blue-skinned or grey, hook-nosed, sometimes with pointed ears and snakes, and he carries a large hammer. What the hammer is for is not certain; it has been read as an instrument for striking the fatal blow, for sealing the tomb door, or simply as a badge of office. He appears on tomb walls at Tarquinia and on painted sarcophagi, often in pairs or with other death demons such as Vanth.
Nearly every menacing modern ferryman-of-the-dead is a blend: the Greek boatman's job, Virgil's squalor, and the Etruscan demon's malice. It is worth separating them, because the Greek Charon is not evil at all. He is a public servant who wants his fare.
Where he ended up
He is one of the very few classical underworld figures to survive continuously into modern folk belief. In Greek folk tradition he became Charos or Charontas, no longer a ferryman but Death himself — a black-clad rider who carries off the young on his saddle and drags the old behind, a figure of hundreds of folk songs and of the moirologia, the funeral laments. That is a genuinely unbroken line from antiquity to living oral tradition, and it does not run through books.
In modern fiction he is the standard toll-taking psychopomp: Dante's Inferno 3 keeps him almost exactly as Virgil left him, refusing to take a living man; Milton and Blake follow. Games and films from Hades to Percy Jackson to Clash of the Titans give him a boat and a fee, usually with a skull face he never had in antiquity. Pluto's largest moon, discovered in 1978 and named Charon in 1985 by its discoverer James Christy — who chose it partly because his wife's name was Charlene — keeps the pairing in the sky.
Which river, whose son, and what happens without the fare
What water does he cross?
The sources disagree, which is itself informative. The Styx is the standard answer in later usage, but the Acheron is at least as common in Greek and is Virgil's river; Aristophanes has him call out for the Lethe plain and other destinations like a ferryman announcing stops. There were five underworld rivers in the fullest scheme — Styx, Acheron, Cocytus, Phlegethon and Lethe — and the Acheron and Styx are real rivers in Epirus and Arcadia respectively, with the Arcadian Styx a spectacular waterfall long reputed to have poisonous water.
Whose son is Charon supposed to be?
Hesiod does not name them. Later mythographers make him a son of Nyx, night, and Erebus, darkness, placing him with the other abstract powers of the primeval dark — Thanatos, Hypnos, the Moirai. That genealogy is a systematising exercise by writers arranging the underworld into a family, not an old cult tradition.
Do people ever get across without paying?
Rarely, and always by force or authority. Heracles crosses by intimidation; Aeneas by producing the golden bough; Orpheus by playing until the ferryman is charmed, in Virgil's account in the Georgics. The point of these exceptions is that they are exceptions — the ferry is a boundary that only the extraordinary can cross alive, and every hero's descent has to solve the problem somehow.
Is the coin ever anything else?
Yes. Excavated burials have produced coins of varying denominations, coin-shaped gold-leaf discs and imitation coins made of thin gold foil, and small objects placed in the mouth that are not currency at all. In some regions the dead were supplied with several coins. There are also graves with a coin placed near the head or hand rather than in the mouth. The variation suggests a widely known story being observed in a loose, local, improvised way — which is how most religion actually works.