Do you fast your aquarium fish?

I have never fasted my aquarium fish before. There have been times where I have been on vacation for a weekend and they haven't eaten, but I have never intentionally not fed them. I wonder what the purpose of this is? My thought is, is that fish are not always hungry and they may not eat the food that is given to them right away. So, what happens is that the food goes to the bottom of the tank and probably makes the tank pretty dirty after a while if the food is not ate right away.