Not only are LDS board games being sold, but software companies are also selling clean, LDS themed computer games. One example is found on Cleanware.com. The game is called Outpost Zarahemla and involves helping "Elder Hero" on his mission to expand Mormon colonies in space. As part of the game, you must help spread the gospel, do family history work, and provide for the various needs of people on your outpost.
There are numerous types of LDS games, the most common is games patterned after old games but with an LDS twist. For example you can buy a chess set at Deseret Book, but the pieces are people from the Book of Mormon, like Captain Moroni, Nephites, and Lamanites. You can also buy a game called Settlers of Zion, which is loosely based on the game Settlers of Catan. There are also educational games, such as Who Said…a matching game where you must match the quote to the prophet or person who said it. There is also an Articles of Faith memorization game.