As an archaeologist, I have always been facinated by ancient games. What were the rules? Who played the game, and why? Did the game have any ritual signifigance?
Here are the games I have found in the BGG database that are quite old, if not ancient.
There have to be more, so please add more to the list. Comments also welcome!
The game was first mentioned by the French traveller Flacourt in 1658. The modern rules seem to be already known in the 1820s as they appear in a Bao poem called Bao Naligwa which was written by Muyaka bin Haji.
Backgammon began appearing in the Mesopotamian culture of Ur around 3,000 B.C. and archaeological digs continue to turn up board games very similar to today’s fast paced and challenging game of backgammon. Backgammon in its early form is the oldest known board game in history surpassing even the game of Chess.
The travels of this gaming idea show up in both ancient India culture as well as Egyptian culture where a variation on the game called “Senat” was popular among both Egyptian aristocracy and the slave population. By the time backgammon reached early Greece, the Greeks decided to lay claim to inventing the game but it was only an adoption of their culture from earlier civilizations. In the Roman version, three dice were employed for the moves and the game was referred to as "Bac gamen" or "back game".
Well there seems to be debate as to when this game originated, but at the least, it's pretty old. During my 2-minute internet search for unsubstantiated facts , I saw claims that it was first played in the 2nd century BC ( http://en.wikipedia.org/wiki/Snakes_and_Ladders) and others citing the 1200's ( http://www.historicgames.com/gamestimeline.html). The board pictured in this post is from 1800. There were also many discrepancies as to the original name of the game. However, the web sites seem to agree that it originated as a form of moral instruction to teach children that good is rewarded and evil punished.
although listed here as dating to 1840, hanafuda probably gradually evolved from the 16th century as japanese card playing adapted to repeated government bans.
also, nintento started out by making hanafuda cards in the late 1800's.
like mahjongg, there are many variations for games played with the deck.
For an incredibly detailed and also amazingly interesting look at the history of games, I recommend two books by game developer/historian/fan David Parlett ( http://www.davidparlett.co.uk/) His Oxford books will give you more information than you would ever want to know about how people have played games throughout time. My library had copies of both of them, and I've seen copies in used book shops for around $5.
, I saw claims that it was first played in the 2nd century BC ( 
Unspecified
Portland
Oregon
Unspecified
Not too long on facts, but the article does have some great pictures of chess pieces, tafl boards, etc.
http://www.archaeology.org/0501/abstracts/games.html
JB
Wyoming
Ohio
Lansing
Michigan