Okay, I guess I'm going to argue for the other side here.
I did some time working in health food stores several years ago when the "Master Cleanse" was becoming a huge thing. People would come in to buy their maple syrup and lemons and rave about how great it was, and how they could feel the toxins leaving their system. (Really? How the hell do you feel toxins leaving your system? Could someone please explain this to me?) And then they would inevitably add, "and I've lost so much weight!" I think that's the key right there. No matter what bullshit people give you about "detoxifying" (and it is mostly bullshit - there's NO evidence that it works, and plenty of evidence that it's actually counter-productive because it puts additional stress on your organs - see here for more on that), as far as I can tell, the bulk of people doing it are really primarily doing it TO LOSE WEIGHT. The stuff about detoxifying is just a fancy rationalization. Of course you're going to lose weight if you consume only lemonade for ten days. That doesn't mean it's good for you. In fact, losing weight rapidly (like, ten pounds in as many days, as I recall a couple of people reporting to me) is essentially never good for you.
I have never tried that particular cleanse, but I've tried a fruit fast for ten days. I did everything I was supposed to, working into it gradually and so on. I felt horrible and got diarrhea. I was told by various well-meaning people that I was supposed to feel horrible, and that that meant it was working. My pounding headache, they said, was from "toxins" (actually, I think it was probably just from not eating properly). That's the really infuriating thing about cleansing and alternative diets generally - it's part of the lore that the automatic response when someone's diet isn't working for them or makes them feel horrible is either that they're not doing it right, or that they're just going through a painful adjustment period as their body rids itself of the effects of their previous bad diet. So, basically, the lore surrounding cleansing (and other alternative food practices) makes it immune to criticism. If that doesn't raise a few red flags, I don't know what does. (Here's a fascinating website with lots of articles about the culture and psychology of alternative food practices.)
Now, I realize that there are gentler forms of cleansing. Some people like to periodically go on a "mono diet," e.g., the brown rice diet, or a diet limited to a few kinds of food. I think this kind of "cleansing" is much more sensible, because you're at least giving your body the calories that it needs to function. I've actually had a lot of success doing a simplified diet of brown rice, vegetables, and tofu. Generally, I think that just eating simple, natural food and cutting out stuff that you already know is bad for you (sugar, caffiene, alcohol, processed stuff, fried food, etc.) will go a long way towards making you feel good, and help you lose weight if that's one of your goals.
I also realize that people have been fasting for millennia, for various reasons. I'm not saying there aren't benefits to fasting - there definitely are. A lot of people seem to get a sort of spiritual "high" out of it. For some people, it's an exercise in self-discipline. Most of us in North America are surrounded by plenty all the time, so it's good to remind ourselves sometimes that we can actually do without a lot of things - that we can not eat everything we want all the time and be okay.
Sorry about my long-winded response, and I'm probably going beyond the scope of your question. I actually get a bit emotional about this topic. In my health food store days, I became very skeptical about a lot of aspects of the alternative diet/health food/whatever-you-want-to-call-it subculture. A lot of people would reject out of hand what conventional medical evidence said because, you know, doctors are all slaves to big pharma and the food industry, but they would unquestioningly buy into all sorts of dippy alternative food fads with zero evidence to support them (and which, by the way, also had an industry pushing them). It made me want to scream. I'm certainly not saying that the standard North American diet doesn't suck, or that people advocating alternatives to it aren't right about some things - I'm just saying that it should taken with a grain of salt (unrefined sea salt, of course), like everything else.
It's also good to keep in mind (to return to cleansing specifically) that there's an industry making money off it in the form of books, supplements, and so on. I think any time there's profit to be made by promoting an idea, it's healthy to be skeptical.