Question: There is a particular recruiting company that continues to contact me. I have been unhappy with their performance in the past and have been clear that I am no longer interested in their services. I have had to inform them of this multiple times.

Whenever they contact me, I inform them that I do not want them to contact me further. They oblige for a few months, and then I get an e-mail or phone call from a different recruiter with the same company. Most recently, I expressed my frustration and insisted that I be completely removed from their database. Today, I received another e-mail from them after months of silence.

Is there any sort of legal grounds I can quote or anything else I can say or do to force them to *actually* remove me from their list of contacts and stop contacting me?

Answer: 
This sounds like a process problem and not just the typical behaviour of individual recruiters. The good ones never waste their time calling people with no interest. There are plenty out there who are. 

Call their office and ask for someone higher up than a recruiter (manager, owner, partner, etc.). They obviously have a problem of not updating their databases. There needs to be some mechanism in their operations to prevent calling people who are not interested to the point you have to take such drastic measures. It sounds like they do a terrible job at this if they make any effort at all.

They're going to ask what recruiter called you; don't tell them. Here's another chance to point out the flaw in their systesm. Why can't they lookup who in their company called you? The goal isn't to punish the individual recruiters, but a company that has implemented poor policies and procedures.

I hate it when customer service people don't have the necessary information to do their jobs correctly and not waste my time.
First step - Check the recruitment companies privacy and/or communication policy.

Second step - For most Western Countries, there will be a Privacy Commissionaire who you can report them too (just make sure you have documented proof that you have requested them to remove your personal details/information from their records)

Third step - Search out and contact the Association body for recruitment/staffing firms (NAPS, ACSESS, REC, etc... and Better Business Bureau).

Fourth step - Draw up a 'Cease and Desist Letter' - would strongly recommend using legal guidance (it might cost but if you feel this strong then it shows you are serious). Each state/prov/country has rules, terms, conditions, and you want to make sure you include terms such as 'breach or privacy', 'harassment' and 'feeling threatened' and 'mental duress'.

Additionally, if you are connected to anyone from that company on social media sites - communicate your intention and desire to be removed from their system, and go as far as disconnecting from them, un-following them, and blocking them.