One of my friends is receiving unwanted email from a big motion picture studio, and can't make it stop.
Continuing to send email to a recipient after they have unsubscribed is lame, and illegal. It is a violation of US Federal Law, just as sending emails without an unsubscribe option would be. But, the fact of the matter is, that for the Average Joe Recipient of an email, there isn't a lot of recourse; no easy option to rain down a hell fire of pain on somebody who won't stop filling your inbox with their unwanted email. And no legal standing to sue -- only ISPs, the FTC or states attorneys general can take action under CAN-SPAM.
So, you don't really have a big stick to wield, Mr. Average Joe Recipient. But, that doesn't mean it's hopeless. Here's what I would do if I were in your shoes.
First, make sure you sign up for lists, register for sites, with a webmail account at some place like Yahoo, Hotmail, AOL or Gmail. Personally, I use Gmail, it's my favorite, mostly because it has wickedly-advanced filtering abilities. But, using a webmail provider's account helps you out, no matter which one you use. See, they really do each have a big stick to use to smack senders around when they do something wrong. And sending you mail after you asked for them to stop is definitely doing something wrong.
After you unsubscribe, the next time you get mail from that same sender at your webmail account, use the report spam button. That button click is recorded by the webmail provider, and it registers a reputational black mark against the sender. Enough black marks get tallied, and boom, that sender finds themselves blocked from that ISP, or relegated to the spam folder. And it's their own fault. A mess of the sender's own making.
AOL, Hotmail and Yahoo also offer "Feedback Loops" to senders. These are mechanisms wherein, when you hit that "report spam" button, notice of this is sent back to the sender, and they are expected to immediately stop sending you more email. If they do send you more email, that's yet another black mark on the sender's record. Mailers tend to pay close attention to these feedback loop reports. And if the sender is using an email service provider (ESP), the ESP probably automatically unsubscribes you, overriding whatever the sender might want to do. Meaning, there's a chance that a sender will stop sending you mail after you "report spam," even if they were ignoring your unsubscribe request previously.
If you want to try to complain to the sender, I would look up their sending domain in the Network Abuse Clearinghouse database at www.abuse.net. Run by John Levine, this is a very popular public database of the appropriate place to complain to. It's used mostly for spam issues, and various spam reporting tools utilize this database to figure out where to send complaints. When you find contact info, send those address(es) a polite note, telling them you're receiving unwanted spam from Company X and explain that you would like it to stop. Be sure to include a copy of the email message in question, including all of the raw message source, and full headers.
Alternately, you can sign up for a service like Spamcop, which helps you report spam, letting you paste in a message you've received and having it route the complaint to the appropriate folks. This can also land the sender on the Spamcop blacklist, providing further negative feedback showing that the sender is doing something wrong. But, this isn't as likely to ensure that you stop receiving email messages; sometimes Spamcop doesn't actually send reports back to the sender, if they don't trust the sender, or don't believe the sender to be fully confirmed opt-in compliant. (Which very few mailing lists are, to be honest.) So, it's something to try, but it's not something personally I've ever bothered with.
Whatever you do, don't pretend that you are an ISP and then try to sue somebody who spams you under CAN-SPAM. James Gordon tried that and was mightily spanked for it.