This game, with an ancestry so old it is another contender for the prize of 'Oldest game in the world', is known by a number of different names in England - Nine Mens Morris or Morelles or or Merrills or Merels or Mill or just plain Morris.
There seem to be two forms of the ancient game of Three Mens Morris; one with diagonals and one without. The diagonals form is effectively the same game as Tic-Tac-Toe or Noughts and Crosses today and a board of this type has been found cut into the temple at Kurna, Egypt (~1440 BC) although this may well have been done at some later time.
According to Thomas Hyde (1908), the Chinese also played the game c. 500BC.
A couple of centuries on, Ovid mentions the game in "Ars Amatoria". Roman boards were usually made of wood or tone although the rich occasionally had boards made of more exotic materials (Trimalchio had one of turpentine-tree and Martial speaks of an ivory board).
The game was widely played in England in AD1300 and visitors to the cathedrals of Norwich, Canterbury, Gloucester, Salisbury and Westminster Abbey can see boards cut into the cloister seats by monks.
Presumably an extension of the simpler Three Mens Morris, a Nine Mens Morris pattern is another of the boards that have been cut into the temple at Kurna, Egypt (~1440 BC). Other boards have been found in Ceylon which were carved during the reign of Mahadithika Maha-Naga (9-21AD). European boards have been found in such places as the first city of Troy, within a Bronze age burial site in Ireland and at the Acropolis in Athens. The game reached its peak popularity in Europe during the Fourteenth Century.
As an old English game, it used to be played with black and white pebbles on a board marked out with a trowel dug into village greens as well as in Taverns on boards marked with chalk on a table. Shakespeare mentioned it in "A Midsummer Night's Dream" Act 2, Scene 1 - "The Nine Mens Morris is filled up with mud" which is what must have happened to the boards marked in the village green when it rained!
There is a version of Nine Mens Morris known as Morabaraba or Umlabalaba, which is still popular and played to competitive level in Botswana and South Africa.
It is played on a board with diagonals but the rules are virtually identical to Nine Mens Morris aside from that.
Masters Traditional Games has a range of nice wooden Nine Mens Morris games.
Masters Traditional Games publishes Nine Mens Morris rules, too.
Merrills research from Kansas