At the bottom of every e-mail you get from most of these websites is an option to unsubscribe or edit e-mail or notification preferences. This may be in very small font but it is there. You can choose to unsubscribe completely or receive only the notifications you choose. This includes e-mail notifications from websites you know you never subscribed to. Below are a couple of images that illustrate this.
This is a screenshot from notifications i get from seesaw.
This is a screenshot from a managebac e-mail notification.
I keep certain notifications because i want to be informed immediately, or because i know i will forget to go to the website to check on something i need to moderate. The choice is yours. You can manage your own notifications. Your inbox does not need to be flooded buy junk.