Great question! As a Registered Dietitian Nutritionist, I classify sugar into 2 groups – natural or added sugars. When counseling patients on a healthy diet, I tend to first focus on added sugars. These are the items you mentioned – ice cream, sugar sweetened beverages – in other words sugar added to products. It is the goal to limit/avoid this type of sugar as much as possible. Naturally occurring sugars, like those found in fruits and dairy, are less of a concern especially when these foods are eaten in their natural state, in appropriate portion sizes for a meal plan. As long as fruit is eaten with in appropriate amounts – such as 4 servings on a 1500 calorie diet – it is part of a healthy diet.
For more information, see: http://www.mayoclinic.org/diseases-conditions/diabetes/expert-answers/diabetes/faq-20057835