If you have spent much time in Christian bookstores, you may have come across board games like Ungame, Bible Mad Gab Board Game or Bible Pictionary. Most Christian board games have been made for protestant churches.
However, Catholics have also shown an interest in Christian board games and recently Sister María Granados, a nun in Spain, designed the game La Alegría de la Fe or The Joy of Life. According to The Local, the game is being sold in Spain and Latin America.
In recent years there has also been an increase in Christian video games. The Association of Christian Entertainment helps advance the Christian video game industry.
Wikipedia has a list of Christian video games.
While the goal of these games is to help Christians learn more about the Bible and grow spiritually, board games have also been used to save lives. Here's some interesting trivia: During World War II special maps were hidden in Monopoly board games sent to prisoners of war to help them escape. According to The Guardian, "shot-down pilots and other captured servicemen managed to break out and some made their way to neutral countries and back home."