I'm a member since 2000. In a nutshell, they give you 11 CDs for a price of 1 (you're billed the full price of the most expensive one among the 11 CDs you select, which is usually $16.98 plus S&H and tax -- becomes something around $20). It really works. :D And you know, you can cancel the membership at any time after you get those 11 CDs in your mailbox. XD I haven't cancelled mine though, because I found the service to be useful... Read on.
The `attached string' is that you have to decline their periodic recommendation called `featured selection' from time to time. About every 3 weeks, they send you a mail catalog along with an order form. If you're not interested in buying anything, you have to specifically say so, either by returning the order form with `I do not want to purchase anything at this moment' entry checked, or by logging onto their website and clicking on the `No, I don't want this featured selection' option. (The website option is much less of a hassle, of course.) They give you 10 days to do so (the deadline is indicated on the order form), but since they send you a reminder e-mail at the same time they send you the mail catalog, it's most convenient to click on the link in the email and follow the instruction to decline the offer right when you receive the email.
If you don't decline the offer within the grace period, they send you the featured selection and bill you. (BTW, the featured selection is always at the full price, usually $16.98.) If this happens, you can call them and make an arrangement to return the CD. The return shipping fee is on them, so the only hassle is to call them and send the CD back. (I never had to do this though, so I'm not sure about the exact procedure.)
All in all, just make it a habit to check your email periodically and log onto their website to decline the offer when they send you the email offer, and you'll be safe.
One cool thing about BMG Music Service is that, along with the each featured selection, they also offer to get other CDs of your choice at a discounted price. Sometimes the offer is conditional and you have to get the featured selection as well (again, at the full price, DUH!), but sometimes the offer is independent and you can take advantage of the offer without getting the featured selection. Indeed, the `American' section of my CD shelf has been filled up with this method. The minimum number of CDs you have to buy at one time varies. Usually it's 3 or so (i.e. you have to get 3 CDs without the featured selection to take the offer), but sometimes it's just one. :D
Oh, and it seems that, if you turn down their featured selections in most cases (as you would =p) but still regularly purchase CDs from them, they eventually `give up' and say `OK, we've put you into our special customer group and you don't have to turn down our featured selections from now on... ;_;' It has happened for me when I was about an year into my membership.