This topic's purpose is to try to categorize 0-player games into genres. For purpose of this topic, a 0-player game is a "game" (if that is the correct term) in which no action or decision of a player can affect the outcome once the game starts.

Here are some example classifications to get us started:

Game of pure chance: The game is solely dependent on randomness. One example would be a game where you flip a coin and win if it comes up "heads". Another example would be the card game War, in which players reveal the top cards of their decks and whichever one is higher gets to put both cards at the bottom of her deck; repeat until one player runs out of cards.

Idle games: Games where the idea is that you just leave the game running and it plays itself. Progress Quest is an example here.

Automatic games: The game plays like some traditional genre, but will complete itself without player input. Automatic levels in certain games with level editors (including Mario hacks and Mario Maker) could qualify if you ignore the fact that the player can mess things up by providing input.

Cellular automata: Game takes place on a grid (or similar), with an initial state set somehow. Then, there are rules which dictate what will happen, with no random element. An example is John Conway's Game of Life.

Kinetic novel: A story-based 0-player game. This could be described as a "game" that is just cutscenes (no gameplay). Alternatively, it could be described as a linear story in the form of a game. Note that, unlike in visual novels, there are no choices to be made, and there's only one ending.

What if the game is of pure chance, but a player still can make a decision. e.g. a player says "odd" or "even" and a random natural number in the range (1,7) is chosen with the player winning if he chose correctly? Would that still be a 0-player game?
If no, what about a case where the player has a choice, like choosing "heads" or "tails", but since the probability of either is 0.5 anyway, his choice doesn't have any effect on the probability of win/loss outcome? Why is that a requirement? Why wouldn't multiple possible endings selected randomly work? Why is the "no random element" a requirement? A (partially) random cellular automaton is a totally valid 0 player game.

No Man's Sky

[url=https://en.wikipedia.org/wiki/The_Settlers_(video_game)]The Settlers[/url] supports a 0 player mode. Mmmm, many demoscenes or Flash animations could be put in this category.
Does a media player bundled with a animation count?

Where I come from, we call them "movies"

Snakes and ladders.

Dear Esther counts as 0 player game?

My thoughts exactly.

There's Snakes and Ladders, where players roll dice and move pieces, but ultimately the game is playing itself without any player agency at all. That would be Pure chance. edit: oops, didn't notice that MightyPinecone beat me to it I think that might fall under dtgreene's Kinetic novel category.

Random Journey

Looks awesome in VR! The gameplay: You have a row of identical plates and have to select one. This grants you a random warrior. The AI does the same. The strongest fighter wins. Repeat!