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.
Play-by-mail game
Correspondence chess has been played by mail for centuries. The boardgame "Diplomacy" has been played by mail since the 1960s, starting with a printed newsletter (a fanzine) written by John Boardman. More complex games, moderated entirely or partially by computer programs, were pioneered by Rick Loomis of Flying Buffalo in 1970. The first such game offered via major email services was "WebWar II" (based on Starweb and licensed from Flying Buffalo) from Neolithic Enterprises who accepted email turns from all of the major email services including CompuServe in 1983.