On the upper bar on all SE sites, there is a "Stack Exchange" dropdown with "hot questions / all sites / inox / notifications" sections. On the bottom of it, there is a "email settings" option with "Email me my unread inbox messages". I'm not getting any email notifications, and my email address is correct in the textfield there. What could be happening?
To expand what I mentioned in the comments, you get notifications of unread inbox messages, not all inbox messages.
(Un)fortunately, clicking on the MultiCollider (aka the Stack Exchange notification dropdown menu) marks all messages as read, which is what I assume is causing you to not get any emails.