Backgammon
Backgammon is one of the oldest known board games. Its history can be traced back nearly 5,000 years to archeological discoveries in the Middle East, originally in Iran. It is a two player game where each player has fifteen pieces ("checkers") which move between twenty-four triangles ("points") according to the roll of two dice. The objective of the game is to be first to "bear off", i.e. move all fifteen checkers off the board. Backgammon is a member of the tables family, one of the oldest classes of board games.
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.