Apples and carrots are really bad snack foods because of their high glycemic index - they have a lot of readily available carbs, so you get a quick burst of energy but then it's gone and you have a rumbly tummy and cravings. It's much better to eat things that you'll burn through more slowly, like proteins.
A string cheese stick can be a great snack, or a couple ounces of chicken breast. I love the South Beach diet books for great ideas on low-carb snacks. I remember doing a lot of roll-ups: a lettuce leaf smeared with some low-fat ricotta and a slice of turkey breast. Healthy and filling!