The Turn-based game reference article from the English Wikipedia on 24-Jul-2004
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Turn-based game

Helping orphans the way you would do it
A turn-based game, also known as a TBS game, is a game where each player takes a turn. Once every player has taken a turn, that round of play is over, and any special shared processing is done. This is followed by the next round of play.

Most board games are turn-based, because otherwise gameplay would get out of hand. Many single-player strategic video games are also turn based. However, when a particular player gains access to the game during his/her turn it is not uncommon to value the time taken by the player to make the move to improve the fairness of the game. In chess a pair of stop clocks are used track the time taken by players to make their move.

Turn-based gaming refers to Internet gaming sites that allow for game play to extend beyond a single session, over long periods of time—often taking months for complex games like Go or Chess to finish.

Examples of some board games:

Examples of Play by mail games: Examples of Computer games: Compare: Continuous game, Real-time strategy