Excluding personal emails, there are two situations where you receive emails from legitimate sources. Either you have signed up to an email list where you are sent copies of all the emails sent to the list or you are a member of a site or organisation that sends emails to its members. The option to unsubscribe needs to differ between these two options but there are many sites where the unsubscribe option doesn't work the way it should.
Where the site is a simple mailing list where you don't have any membership of anything beyond receiving the emails then the unsubscribe process should be very straightforward. All of the emails you receive from that list should have an unsubscribe link at the bottom of the email. When you click that link you should be automatically unsubscribed from the list. In some cases the emails to be sent out might be prepared in advance and sent out in batches over a day or two but as you have presumably just received the email you want to unsubscribe from there shouldn't be any waiting to be sent to you. At worst if you delayed unsubscribing until after the next email had already been added to the queue for sending then you would at most receive one more email after unsubscribing.
There should not be any need for you to re-enter your email address to unsubscribe. The unsubscribe link should already identify who you are so that it knows who to unsubscribe. Those that do ask for your email address to unsubscribe you are not providing a proper unsubscribe link and so can be treated as spam.
Also they should not be sending you an email telling you that you have unsubscribed - that email is definitely spam.
Those where the membership goes beyond the email list are a little different. In these cases receiving the emails may be a condition of your membership. In that instance you would need to cancel your membership in order to 'unsubscribe'. Where the emails are not mandatory there should be an option on the membership site for determining which emails you get. If there isn't an actual site associated with the membership then the emails should work just as if they were a stand alone list.
Where the emails have an associated site then a link to log in to change your membership settings may be reasonably substituted for the unsubscribe link. After all they need to know whether you are just unsubscribing from the emails or whether you want to cancel your entire membership. In this case you will be required to login to your account in order to change the settings appropriately. This is assuming that there is something of significance that you get for your membership other than the emails as the emails are in these cases a minor part of what you get (if they are not then they are just an email list and should have an appropriate unsubscribe link).
There are plenty of sites around that send emails that don't follow these rules. They provide just the emails and no way to unsubscribe just by clicking a link or they require you to login to unsubscribe where there isn't anything of significance in the member account other than the emails. In these cases the email providers deserve to be reported as sending spam.