The term zero player game refers to a game in which the player(s) are not necessary to play the game, and are only there for their own enjoyment. This generally means one of two types of games:
Games of Chance: Games such as Snakes and Ladders, War (the card game), Bingo, and the lottery allow for essentially no meaningful strategy. The spirit of the game is that you set up, take the knocks as they come, and have some fairly mindless fun. Some games may be treated as zero player games if the players are sufficiently sophisticated; for example, Tic-Tac-Toe is a fully solved equation for most adults who care to play the game, and therefore can be seen not as a game of chance, but a game of no-chance.
Automated Games: Games such as Conway's Game of Life are also often referred to as zero player games, as all 'play' takes place without any player involvement. The player sets up the initial conditions, and the computer runs the program. This has been used to good effect in computer games like RobotWar (and the related C-robots and RoboCode), and indeed in the real-world Robot Wars, in which the player designs a 'robot' and sets it free in a field of battle to see how it does. This sense is used most often in computer programming, and the seminal work on the idea is Staffan Björk and Jesper Juul's Zero-Player Games. They identify a number of types of zero player games, including Checkers and Chess games played by AI players; "Setup-only games", such as the Game of Life; and games that fall under the 'Games of Chance' (or no chance), as defined above. They also note that many computer games have zero player segments, where the player can sit back and let the computer take over the play for a bit.