Twilight Struggle
"Twilight Struggle" was the highest-ranked game on BoardGameGeek from December 2010 to January 2016. As of August 2018, the board game occupies a fifth spot. Being released in 2005 it is the oldest board game in the overall top 10 ranking.
Backgammon
The history of backgammon can be traced back nearly 5,000 years to its origins in Mesopotamia (modern-day Iraq). Excavations in Iraq have shown that a board race game existed there around 5000 BC. The world's oldest set of dice (made from human bone) were recently discovered in that part of the world. Modern Iraqis continue to enjoy playing the game. 
The Royal Game of Ur, originating in ancient Mesopotamia before 2600 BC, may also be an ancestor of modern-day table games like backgammon. It used tetrahedral dice. In the modern Middle East, backgammon is a common feature of coffeehouses. Race board games involving dice have a long history in Iraq, including the Royal Game of Ur in Babylon. Today the game is commonly played in Iraq, Lebanon, Egypt, Syria, Jordan, and other Arab countries.