From my point of view, eating before and after exercising is essential.

Many people have the misconception that not eating before working out will burn more fat, but this article on MSN suggests that it is not true:

Even though the body has plenty of fat stored, for fat to be “burned”, or metabolized, carbs need to be present. Often, the liver’s carb stores are nearly depleted by the morning, so many people may wake up in the morning in a state of energy deficit, where there are not enough carbs to provide energy and to help utilize fat. So they need breakfast to infuse more energy into their body.

Of course, this doesn't mean you should have a large meal before working out, unless you want to be nauseated! :) My advice would be to have a small meal with some carbs to fuel your body during activity, not forgetting to favor "good carbs", such as whole grains, fruits, and juices, over junk food.

Proper nutrition after exercising is also quite important - during a time window which lasts about an hour to 90 minutes after working out, body enzymes which replenish your energy storage will be at their peak. This is the time to get some high-quality protein and carbs as well. Even if you don't feel hungry, especially after a hard session, try grabbing a sports drink on your way home!

Do what works for you. Everyone is different. I like eating about an hour before working out then hitting a protein shake post workout.