At a prior employer, we noticed that there were many customers getting essentially free service ($100-200 per month) by calling customer service hundreds of times per month and asking for credits for all sorts of things. They were generally very nice and just picked up $5-10 credits until their service was free. Beyond the free service, they were costing the company the expense of the service calls.
We started routing all of them to a small group of agents and flagged the accounts so the agents would deny them pretty much every time. It was kind of funny because we didn't tell them anything changed, but you could see that some of them noticed because they started asking which call center they were talking to. They would immediately hang up and call back over and over and just keep going back to the same place. Eventually most of them gave up.
Note: nobody here would/should feel sorry for this particular company, but I still thought it was funny to see these scammers get mad that we caught on to the scam.
At my old company we would ban customers that were repeatedly abusive to customer service agents. Agents had the right to hang up on customers that were being abusive and if the same customer kept getting reported, eventually they would receive a letter from the legal department telling them to stop. If it continued, they would get banned.
I remember one guy was so bad that a director got the phone system to automatically route any calls from him to his mobile line and put him in his phone book. He would very politely greet him by name as soon as he picked up the call to make it clear that he wasn't ever going to get through to anyone else.