In view of the constantly recurring speculations, it seems a good idea to post a variety of the versions, with dates. The earliest dated "Ring Around the Rosie" is ca. 1790 (and this reference can't be found now) as suggested in this rhyme from Massachusetts:

Ring a ring a rosie,
A bottle full of posie,
All the girls in our town,
Ring for little Josie.

Published 1883:
Round the ring of roses,
Pots full of posies,
The one who stoops last
Shall tell whom she loves best.

Also published 1883:
Ring around the rosie,
Squat among the posies,
Ring around the roses,
Pockets full of posies,
One, two, three- *squat!
(this one still used in Georgia in the 1930s. "Last one squats will be old Josie" is the end of one from Texas. Also see the one from Switzerland)

1840s, acc. to W. W. Newell:
A ring, a ring, a raney
Buttermilk and tansy,
Flower here and flower there,
And all- squat!

The above all from W. W. Newell, Games and Songs of American Children, 1883, (1903), Dover reprint.

Now a few from the other side; from the Opies, "The Singing Game."
1880s, Lancashire:
A ring, a ring o'roses
A *pocket full o' posies- *or bottle
Atch chew! atch chew!

1881, Greenaway, Mother Goose:
Ring-a ring-a-roses,
A pocket full of posies;
Hush~ hush! hush! hush!
We're all tumbled down

Shropshire, 1883:
A ring, a ring o' roses,
A pocket full o' posies,
One for Jack and one for Jim
And one for Little Moses!
A curchey in, and a curchey out,
And a curchey all together.
(Children curtsey at end. See the Italian one)

ca. 1900, Italy:
Gira, gira, rosa,
Co la più: bela in mezo,
Gira un bel giardino,
Un altro pochetino;
Un salterelo,
Un altro de più belo;
Una riverenza,
Un'altra per penitenza;
Un baso a chi ti vol.
---
Ring a ring a roses
With the most beautiful in the middle;
Ring a pretty garden,
Another circle round,
A little skip,
Another even better,
A curtsy,
Another for penitence;
A kiss for the one you like.

1857, Switzerland:
Ring-a, ring-a, row,
The children go into the greenwood,
They dance around the rosebush
And all *squat down.

Above all from Iona and Peter Opis, 1985," pp. 219-227, "The Singing Game."

A simple little children's game, with its many variants, has picked up all sorts of baggage from speculation. The rhyme is lost under the load. Even the Opies couldn't resist and piled on their own supercargo-
"Thus in 'Ring a Ring o' Roses,' we have, or so it seems, a spray from the great Continental tradition of May games, that preserves the memory, however faintly, of the rose as the flower of Cupid, the wreath of roses with which Aphrodite crowned her hair, ...."


Now the relation to-
Ring me, ring me, ring me rary,
As I go round, ring by ring,
A virgin goes a-Maying,
Here's a flower ...... etc.