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.
Netrek
Developed as a successor to 1986's "Xtrek", "Netrek" was first played in 1988. It was the third Internet game, the first Internet team game, and as of 2011 is the oldest Internet game still actively played. It pioneered many technologies used in later games and has been cited as prior art in patent disputes. "Xtrek" and "Netrek" are the oldest games of what is now called the MOBA genre.