Native push notifications without any 3rd party extensions or services.
Seamless integration with Zapier. Would allow to connect any WordPress action to any Zapier-enabled service.
Would allow to publish posts on Facebook.
Would allow to publish tweets on Twitter.
To attach and send files directly in email.
To publish WordPress posts or users upon any Notification action.
To quickly disable Notifications for specific pages or users.
BuddyPress specific triggers.
Integration with OneSignal to send push messages via their API.
Digest email notifications
To send notifications once every while, ie. if post has been updated dozens of times during a day, one email would be send the next day morning with all the changes log.
Easy Digital Downloads
Easy Digital Downloads integration with specific triggers.
Integration with MailChimp service - send email to a list or save contact to specific list.
Statistics and insights for each notification, would allow to see how often the notification is sent or when it was sent the last time.
To click a button and fire notification.
Frontend and backend notifications
Something like push notifications but displayed within a page. Would allow you to show in wp-admin that new comment has been published or show to all your users that a specific product has been just purchased.
Would allow to create webhook URL and fire your own notifications upon receiving a request.