Many people will participate in a "cleansing fast" in an effort to feel better or lose weight quickly. I've heard of people who went on a liquid diet for over four weeks straight. No solid foods at all, but could eat anything as long as it was pureed first. Yes, that meant they could eat a BLT, as long as it was blended into a liquid first.
Personally, the idea of a fast seems bad. Your body needs food for the fuel and nutrients it provides. Yes, you can survive without food for long stretches of time, but that doesn't mean you SHOULD do this to your body. There aren't any studies on how these fasts affect the toxins in the body that are claimed to be "cleansed" during the fast. Many people fast for the spiritual and psychological benefits. This has a longer history and some better evidence supporting it.
One of the most vocal advocate of fasting is Gwyneth Paltrow. Over the years, she has recommended different plans for her annual fast. She recently said "I'll wake up exhausted; I can feel my adrenal cortex being really high. When I get into bed, my heart will pound, my skin won't be good, I'll feel cranky, and then I'll just know it's time." This from the same woman who may have been hospitalized because of a fast four years ago.
As always, our goal should be health, not just skinny. We should aim to be strong and well. That will lead naturally to a good weight for us. Personally, I like food way too much to avoid it without it being an emergency.