Actually, eggs aren't bad a few times a week. It's the bacon and sausage that go with them that is bad, bad, bad...

Eggs are an excellent source of protein and antioxidants, plus omega-3s.
We are FAR from being health nuts at my home, but I do try to make sure that my kids eat okay for breakfast and dinner *most* days of the weeks. Sure, we have our bad days but we aren't consistent with bad days.
What do I think constitutes a healthy breakfast? Here's what I usually fix.
Cereal (1 day a week). Usually when I'm rushed. The only one they get (that they like) for breakfast is Life cereal. Not "healthy" but not "unhealthy" either.
Scrambled egg with toast. DD sometimes asks for a bit of cheese on top or salsa.
Pancakes that I make myself (not frozen). I can control the amount of sugar and fat in them. Also give a limited amount of syrup. Honestly, though, they aren't "up there" in the health department but better than some meals.
Once in awhile I will make creamed chipped beef over whole grain toast. I use skim milk to make the sauce. Again, not healthy but I don't think it's horrible.
For some reason, I feel a lot better about those meals than I do "frozen french toast sticks", Pop Tarts, and Fruit Loops. I guess I have a problem with *candy* for a meal.