I eat an egg-white omelet most days on the ship. There is always an omelet station set up at the end of the Topsiders buffet lines (between the two actually, where they do sushi in the afternoons.) You can always request egg-whites. Some days they have their featured omelette made out of egg-whites, other days I just make one up. Parrot Cay usually has an omelette station on the days they have the breakfast buffet. I think you can also request egg-whites when you order eggs for breakfast at Lumiere's.
Other healthy options include muselix, yogurt, turkey sausage or turkey bacon (sometimes), fruit. You can usually order V8 as well, even when not listed as an option. Lumiere's breakfast has several healthy sounding options, including yogurt/granola type drinks, oatmeal, and healthy breakfast combos.