Well it's better to unsubscribe from the email service to stop receiving the emails.
Once you have opened the email, at the FOOTER of the email you will see unsubscribe option to stop receiving mails from the service. Just unsubscribe and you won't any emails further.
For example if you want to stop receving notifications from Hubpages, then open an Email from Hubpages and then scroll to the footer and you will see
"Please do not reply to this message, it was sent from an unmonitored address.Unsubscribe from all HubPages emails"
Just click on Unsubscribe from all HubPages emails and you will not receiving notifications from Hubpages.