Backgammon
Backgammon is descended from much older board games from Africa and West Asia like Senet and Tabula and Nard. It's probably most closely related to the Royal Game of Ur, played in Sumer and in Shahr-i Sokhta (in modern Iran) about 3000 BC.
A project making a backgammon board
Chess
Other board games
Athletic games
Dice games
To find out more about ancient and medieval board games, check out these books from Amazon.com or from your library:
Kids
Around the World Play!: The Best Fun and Games from Many Lands,
by Arlette N. Braman (2002). For kids. There are lots of ancient games
in here too, even though the title doesn't say so.

