Simple answer is no.
For short runs of less than an hour, you certainly do not need to fuel. On longer runs - even ultra marathons - you do not want to eat immediately before running. Instead, on longer runs it is best to fuel on the run either through liquid calories (preferred) or small portions of solid calories. Depending on body size and effort you should consume about ~240 calories per hour during workouts longer than one hour. Your body can sustain itself in this for hours on end.
If you choose to eat before you run, let it be at least 2-3 hours before hand. If you feel like you absolutely need to eat something before a short run, try drinking a glass of water.
On the run fueling options are plentiful. I recommend sticking to products containing natural ingredients (skip high fructose corn syrup products). Some recommended vendors and products are Hammer Nutrition's HEED, PowerBar Perform, Infinit Nutrition, ClifShots, etc.
And I would absolutely recommend fueling with 20 minutes AFTER running. This is the time that your body will be best at absorbing fuel to help you recover and rebuild your glycogen stores. A recovery meal/shake/drink should be somewhere around 200-300 calories depending on body size and duration of exercise with about 20g of protein. The vendor's I mentioned above also have some quite good products for recovery.