Redmine

Perhaps with the exception of password reset emails?

Yes, definitely.

I was thinking that the user should have an additional option of "No notifications" in the Email Notifications section on the My Account page. This would suppress issue and other event notifications, but not administrative emails such as password resets.

Temporary workaround for us: http://blog.goyello.com/2009/07/16/how-to-manage-email-notifications-within-redmine/

Duplicate of An option to completely disable email notifications