I do not personally believe in fasting, or see it as having any big advantages by itself. Still sometimes I will fast my fish for a variety of reasons. When I go on vacation, I often fast them, because if I get an auto-feeder, there will be waste and no one there to clean the water. Also, if I am very busy one week and do not change the aquarium for my water, I may fast them, because it results in less waste, which keeps the water a lot cleaner.
However, with that said, I still have yet to see definitive proof or results that fasting fish for a week or two at a time really helps them with anything.