>>> . . . others I don't recall using at all
Those words might be the clue to why the amount of spam you're receiving has suddenly increased.
I get loads of emails from companies such as Ryanair, easyJet, Eurostar, Rakuten, Amazon, Tesco, Waitrose, etc. I'm confident that clicking the 'unsubscribe' button in any of those mails would simply have the desired effect (because they're all reputable companies).
However, as Tuvok suggests, clicking on the 'unsubscribe' button on a spam email is pure madness. Spammers send out millions of emails to 'guessed' addresses (such as
[email protected],
[email protected],
[email protected], etc) in the hope that at least some of them will be delivered. However what they'd really like to find are email addresses where their spam will
definitely be delivered. Clicking 'unsubscribe' on one of their emails effectively sends back this message "Hi. Yes, this address really exists. Please send me a few million other spam emails".
If you're using an email client (such as Outlook Express, Thunderbird or Window Live Mail) you could give Mailwasher a try. (It 'learns' what is, and isn't, spam and attempts to block it):
http://www.mailwasher.net/
If you're using webmail there's nothing you can do except (if the problem gets really bad) changing your email address. That can be less hassle than you might think. For example, you get a free email account here
http://www.gmx.co.uk/
and then use the 'mail collector' facility to get mail from your old account forwarded to it. (It goes to a separate inbox, so you can easily see which address the sender has used for each email). You'd still get the spam forwarded but once you were sure that all of your genuine contacts were using our new address you could then disable mail forwarding and get rid of the spam.