Few things in English folklore are repeated with more confidence than this. Ring a Ring o' Roses, the circle game every small child knows, is "really" about the Great Plague. The rosy ring is the rash. The posies are herbs carried against the smell of disease. The sneezing, "atishoo, atishoo", is the final symptom. And "we all fall down" is death.

It's chilling and memorable, and folklorists don't believe a word of it.

Why it's wrong. First, the dates. The plague of 1665 came nearly three centuries before anyone made the connection. Wikipedia notes that writers on the rhyme before the Second World War never mention plague; the reading spread afterwards. By 1951 it was widely accepted, and Peter and Iona Opie, leading authorities on nursery rhymes, described its believers as "would-be origin finders".

Second, the words. The rhyme doesn't appear in print until the 19th century, and early versions vary. Kate Greenaway's 1881 Mother Goose has "Ring-a-ring-a-roses, / A pocket full of posies; / Hush! hush! hush! hush! / We're all tumbled down." There is no sneeze. An 1855 version has "Laps full of posies" and "Awake – awake!" The lines the plague reading depends on are missing from many of the earliest records, and Wikipedia notes the symptoms don't fit the plague closely anyway.

Third, as Snopes points out, a rhyme supposedly sung since the plague years would surely have been written down at some point in those centuries. It wasn't.

What's actually known. The origin is unknown. Descriptions first appear in the mid-19th century, and there are variants in Britain, America and across Europe. Snopes calls it a nursery rhyme of indefinite origin and no specific meaning. It's a game: you hold hands, go round, and fall down laughing.