What are people's experiences with forks? What are some of the most successful forks? When is it appropriate to fork?
It's obvious that you're using the 1st meaning but it's worth clarifying because there's a lot of grey area here.
Are you forking the project to make a small change and submit it upstream? (the friendly fork)
Are you forking the project to have a playground for new ideas and experiments? (the playground fork)
Are you forking the project to deploy custom patches while you wait for upstream to fix a bug or add a feature or cut a release? (the pragmatic fork)
Are you forking with the intention of using that code to bootstrap the creation of a entirely new and unrelated product? (the bootstrap fork)
Are you forking with the intention of maintaining the existing product with a new direction because you don't agree with the authors? (the hostile fork)
Are you forking with intent to burn most of existing codebase to the ground and build it back up from scratch to compete in the original domain? (the competitive fork)
Of these, I think the friendly, playground, and pragmatic forks are generally seen as positive since the original project and its users can benefit directly. The bootstrap fork is neutral, no harm but there is an opportunity cost and occasional whining from rent-seekers or copyleft purists. The hostile and competitive forks are generally a negative since it implies a community schism and should be avoided unless there are solid technical benefits that cannot be achieved through existing means.