I am on several different forums relating to my different interests, and if I were to permit email notifications I'd be swamped by them! That is one of the first things I make sure is not ticked "on" when setting up my profile after registering and joining a new site. Just on the off-chance that somehow things slip through anyway, though, and that has happened occasionally, I provide a different email address than my customary one that I use for personal email interactions. And, yes, definitely official mails from the admins/moderators of a site are permitted, which makes good sense.
As for notifications/alerts here, too, I have that turned off as well, as again I don't need to know that so-and-so is busily posting up a storm while I'm on here reading posts and posting. When I get around to checking the threads I "watch," which of course includes those in which I have posted, and in which presumably I'm interested, plenty of opportunity to see new posts by whomever at that time....