Spam stops when it is no longer profitable. Spammers see their profits plummet when no one buys from them (because you don’t even see the spam). This is the easiest way to combat spam, and certainly one of the best.
You can also affect the expense side of a spammer's balance sheet. If you complain to the spammer's Internet Service Provider (ISP), he will lose his connection and may have to pay a fine (depending on the ISP's acceptable use policy).
Because spammers know and fear such notifications, they try to hide. That is why it is not always easy to find the right ISP. However, there are tools like SpamCop that simplify reporting spam in the right way to the right address.
How does SpamCop find the right ISP to complain to? It looks closely at the header lines of the spam message. These headers contain information about the path an email has taken.