That's only true of the dubious "viagra" style spam, where they got your name from a list. I don't think those even bother with "unsubscribe" links any more. I only see unsubscribe links from places where I've had to give my email up to buy something or sign up to a site. Those are generally legit and most of the techy/startup web sites will unsubscribe you immediately.
The next tier are the sites that unsubscribe you but take more than a week and will keep spamming their dumb newsletter in the meantime.
The final ones are either broken by stupidity (it's amazing how many web developers cannot grasp that "+" is a legit email character), or willfulness and will keep spamming no matter what. I block these at the SMTP level with 503 messages (usually containing some personal insults and swearing) as soon as they "RCPT TO" the unique email address I gave them.