I saw a great documentary this year about fasting and its benefits. Apparently scientists in the USSR discovered potential benefits for treating a number of diseases this way, and there still are a number of "fasting centers" spread throughout Russia. People there fast for 2 weeks, nothing but water... They interviewed some of the "inmates" and they were mostly feeling great. They could even perform physical activity, and some said they could have lasted longer than 2 weeks.
Western scientists are only starting to research this (limited scientific interest so far makes sense: no company would have an interest in financing research on the benefits of fasting!!) But it is promising. If I recall correctly they performed tests on cancer stricken rats. Half the rats underwent chemiotherapy in a well fed state. The other half, after fasting for 48 hours. Apparently the fasting rats not only managed chemiotherapy side effects better, they also fought off cancerous cells more efficiently.
We still need a lot more research on fasting, that's for sure. But in my opinion the benefits are only logical: from an evolutionary perspective, our bodies are a lot more used to dealing with food scarcity than with an abundance of food.