How do I make a MyBB website and not take people's emails? Is that possible?
Would it require a mod? Is there such a mod?
why you need such setup ! anyway, you have to experiment for it. see
replies here
It would definitely require modifications of the software. I'm not sure a plugin itself would do the trick.
Thought: If users have no email, how do they reset their passwords?
You can use a custom registration form that will enter a dummy e-mail account. That would be fairly easy to do but like others have said, it will pretty much break any feature that utilizes it.