It seems that in the Middle Ages, people would scratch playing boards onto tables and benches here and there, and could play with coins or other found markers. If they had chess pieces that was fancy, but if not they could play draughts ("drafts," for Americans, who call it checkers anyway, and according to the site linked below, it's also called checkers in Australia and Canada).
Checkers is described well here, and a game called "halma" which uses a checkers board and pieces, but is played from one corner across to the other, like Chinese Checkers, without jumps but not captures.
|Posted on the local Mac Users' list:
Most interesting article on computer/checkers:
or more modern, bought or electronic