Since some people have mentioned multiplayer games that can be set to bots only, I have one that I remember enjoying many years ago:

Tetris Attack

In Tetris Attack, the options menu allows you to set both players to be AI controlled. This can be done in any mode, including the single player modes; however, if "you" beat story mode this way, the game won't show you the ending, but will instead tell you to turn this feature off.

I wanted to add to this thread something that's not quite a 0-player game, but in the realm. While I don't enjoy this specific implementation, I'd love a game that does it better:

Gratuitous space battles. It's interactive (so not really zero player) in that you set up your roster and broad tactics, then hit play and it resolves. There's no intervention once you hit play -- just watching to see how it resolves. How do the rest of you feel about that in the family of "0-player" games? Any others like it for you to recommend?

EDIT: Majesty is in this family, but only loosely. There's too much regular player activity in between the heroes going out and doing what they do to call it as having "0 player" moments even though. (I didn't play Majesty 2 yet...).

Anything new in the last couple years in the 0-player game realm?

Adding on my previous, the one Driftland: Revival is another game like Majesty that, while not making it a 0 player game, you do not control your units but only ask them to do things. It's not as elegantly done as Majesty was.

0 player games? that sounds stupid
why would anyone want to "play" such games?

Philosophic question: can it be called game if it has no player?
I think a game requires interaction by definition. Nitpicking though, I understood what you meant in the OP. :P

clearly not thats why visual novels are not games , you can just press auto and they play themselves out

Or walking simulators. After all, for those the only affect you have on the game is how long between story events.

yeah those too, I hate them :P they are just time wasters, oh look so beautiful graphics and environment, press W for 30 mins to see the same until the next stage
tbh i don't even like the cutscene heavy ones like that kojima fedex simulator game, they should make movies, but not this half movie half game thingy

Some of the examples mentioned are definitely games. Although employed for a different reason in 0-player mode. You probably would agree that chess and Go are games. Even games that predate the computer by many centuries. And yet, 0-player mode was essential in developing a Go-engine that could beat humans through machine learning. They pitted several instances of machine learning code against each other and against the best human written codes available. The only input parameters to the machine learning programs were the rules. Millions of 0-player games later the code of the machine learning system had evolved to a playing strength way beyond any human capability.

Conway's game of life is also very interesting for investigating the phenomenon of emergent complexity. But again, that's more a scientific tool (and nerd toy) than a proper game. Still very fascinating!

This can be done on some S.T.A.L.K.E.R. mods in warfare mode (a mod / addon for others that changes areas on the map to bases, resources and territories) - though I think it requires console / debugging commands so doesnt entirely fit.
I wasnt aware of this. might give it a whirl and see if it finally helps me break the barrier of getting into it somehow.

Because they're fun to watch?

It's fun to load up John Conway's Game of Life, set an initial condition, and watch things evolve.

Totally fits! Care to share more about it? That sounds like something I'd like to play with. I love setting up scenarios in Civ4 and then watching which AI edges out victory.

You may mean to say "decision" instead of "interaction".

but they are not fun to watch, just a waste of time