I agree that all alerts should be available for email notification. It helps to make the community feel more active and alive, and members feel like to feel a part of that. People using social media already receive many notifications and are addicted to them.
Sure some people will feel overwhelmed (personally I'd rather not receive so many emails) so give them the ability to opt out in every email and their account settings. Having options in the ACP so admins can choose which their forum sends out is essential too. Another option for busy forums is to send them in digest format at specified intervals.