We have a couple of users who are becoming a real pain in the neck because their email accounts are constantly overflowing and sending bounced email messages to the server. They are good members and always responsive about taking care of the issue. But apparently their a little slow because a week or so later the issue happens again.

Is there any way to make it so EE will never even try to send them emails?

I should specify that I have unchecked everything under the email settings in the CP

Go to their user account and look under Email Settings for the “Enable email notifications by default when you post messages” option.  Uncheck it.  Then when they post comments they should no longer receive notices by default.  You can also look under View Your Subscriptions to unsubscribe them from existing notifications.

There isn’t, however, a way to just say “don’t ever send this user emails even if they request to receive them”.

I have done this and it has worked for some of them but others like the notifications but don’t check their email often enough.

I guess then this would be a feature request. I’ll repost it there. Thanks Chris.

Well, personally, I think this falls under “responsibility of the user”.  If they don’t bother to check their email then why would they even want notifications?

Amen.