When my daughter was little, she went through a phase where all she wanted was yogurt and scrambled eggs. Her pediatricain said to let her have what she wanted, as long as it was good for her, but to continue to offer small amounts of other things. He also recommended adding a multi-vitamin to her diet, and NO junk food. No chips, no cookies, no candy, no soda, no "juice drinks" (the ones that are only 10% juice and the rest water and high fructose corn syrup).
I let her eat scrambled eggs and yogurt until she got tired of it, and she started trying some of the other things I put on her plate. If she was thirsty, she got water, milk, or 100% unsweetened fruit juice. She liked the taste of V-8, but not the thickness of it, so I thinned it with water for her. Between meal snacks were bananas, raisins, apples, or other real fruit (not Fruit Rollups), a bagel with cream cheese, or whole wheat bread with natural peanut butter - yes, you can get peanut butter without added sugar (and without artificial sweeteners either - just pureed peanuts with their own oils retained to make it spreadable) at Albertson's.
By the time she was 5, she was raiding the dinner salad and stealing the mushrooms. She's now 17 and has better eating habits than most of her peers.