I had an experience that I laid out in another post, and it's more or less what the original poster outlined, so I won't go into the details again. What I will add, if it hasn't already been mentioned, is the way I got the company in question to not charge my card, refund the initial fee and unsubscribe me from their service. It might seem obvious, even if it is tedious.
First off, don't take "no" for an answer. You will probably have to call their call center more than once. It took five calls in my case. They will probably be reading off of a script. They've heard your complaints before. Two times, operators hung up, and once, the transfer simply dropped the line. They will offer you appeasements. One operator offered a free month's refills, or to negate the price of the initial kit while retaining the subscription fee. I was finally offered half my money back in an attempt to placate me. Absolute refusal to accept any of these half-steps was my only response. You have to be perfectly clear about that, or they'll take it as submission. My wife was calling them before I got home that day and "bless-her-heart," she was not being firm enough.
Side-note: Be polite. My wife was hung up on most likely because she was fuming at them.
Secondly, ask to speak to their supervisor. This might cause some confusion (the first guy I talked to didn't seem to know who his boss was, nyuck yuck yuck). Keep asking. If you can't get higher up the food chain, they will have to start dealing with you more directly.
Third, don't bother making threats, simply state what you will do if they don't do what you want. I said I was going to call my credit card company, I was going to call the better business bureau, and that I would rather close out my line of credit than let them charge another dime. I wasn't lying.
Finally, make sure you get them to clearly state what they are going to do for you. I wasn't satisfied until I made the guy on the other end of the line tell me his name, and what he was going to do (twice). If you get off the phone and there's any doubt in your mind, call them again.
I know it isn't exactly ingenious, but it worked, and I hope if you're the victim of one of these scams it can work out for you, too.