But definitely make sure you're hydrating before you start. You'll be dehydrated because you haven't had anything to drink for however long you've been sleeping. Drink at least 8 ounce of water when you first wake up. You could drink a sports drink before your run so you know you're at least getting some calories. You should also drink water during your run if you're running longer than 30 minutes.
If you're running longer than an hour or doing a really intense speed workout, it's best to force yourself to wake an hour and a half early or more (you could always go back to sleep!) for a small meal. Eating a 300-500 calorie breakfast of mostly carbs will ensure you're not running on fumes. Some examples of good pre-workout fuel include: a banana and an energy bar; a bagel with peanut butter; or a bowl of cold cereal with a cup of milk. If you're eating less than an hour before your run, aim for a light, 200-300 calorie snack such as toast with peanut butter or a cup of yogurt.
Some people can get away with not eating at all before a run of any distance, but you'll run stronger if you eat something before. If you're doing a long run and you really don't have time or your stomach gets upset if you eat before running, try eating something small, such as an energy gel, about 30 minutes into your run.