It is Important
From everything I have read, breakfast is very important!! If you don't eat, you will slow your metabolism down which slows your weight loss. It's one of the worst things, if not worst thing to do when trying to lose weight.
I read, several months back (and I have looked for the post but couldn't find it), about what to do about breakfast and someone mentioned that they treat breakfast like a first lunch. You train yourself out of the mindset that you have to eat 'breakfast', you just eat lunch when you wake up. So, make yourself some soup, have a salad, anything you eat normally at lunch.
I haven't been able to do that, but it is something I am working on now that I am back on track. I can only eat eggs so many times before I am sick of them, and honestly, breakfast is the hardest meal for me! I eat yogurt, cottage cheese, peanut butter on some celery, sf pudding, jello and today I even had the dream cheesecake for breakfast. You should definitely eat something to get your body going.