First off, don't unsubscribe you are just giving them proof that your email address is real. They will continue to spam you even more. If you sign up at a website (like a newsletter or other website), you are bound to get more spam advertising.
Depending on what email you have, you can add them to a blocked senders list or turn on a junk email filter that can delete them as they arrive or move them to a spam folder so you can gaze through them to see if there are any legit emails.
You can't really sue these spammers because there is no way to track them down. Most use email address that are spoofs of others and most of the email addresses don't exist.
Unfortunately, spamming has become common practice like sending viruses, etc on the internet. If you work for a company, you have to understand they don't blocked every kind of spam because there is only so much filters can do. You'd be amazing on how much spam is blocked from your email.
Yes, it is harrassment. You are not alone, but I've gotten used to it. If you use a free account on the web for mail, you can always get another one.