Breakfast, or quite literally, "the breaking of the fast" should be eaten once you are hungry. Your fast will be broken whenever you eat.
That being said, here are a couple of scenarios where you should break regardless of your hunger level:
1) If you are at your goal weight, and know that you will not be able to eat again for 10+ hours, then you should eat in the morning
2) Coming off of an 18 hour fast (some people swear by the breakfast only fasts, for me dinner to dinner works better)
3) After a strenuous workout -- You need the protein
4) Eggs, bacon, and sausage are sitting in the fridge and close to their expiration date -- It's just a sin to let good food go to waste.
I'd rather wait to eat when I start feeling hungry, but I am so grumpy in the morning that I always eat as soon as I get up in order to make up for the fact that I had to get up, and to put off getting ready for work.
The purpose of breakfast is to replace your energy (and insulin stores, protein breakdown, etc) that was used to help heal and repair your body during your nights' sleep. So, ideally you will consume a protein as part of your breakfast and some form of carbohydrate (whether you still consume grains - whole grain whole wheat including the germ OR lots of veggies - spinach, sweet peppers, etc, or a sprouted grain - ezekial bread) in order to help the body repair. It is also important to consume lots of water in the morning to ensure you prevent dehydration for the rest of the day.
Hope this helps!
While I second what others have said, I'd also like to add that it depends on how often you will be eating, or want to eat. It seems to me that meal frequency is also something we all have to figure out. So if, for instance, you do best on two larger meals a day, or maybe even just one, then it's important to eat when you are hungry, but also at times that mean you have the most sustained energy (which can vary from person to person).