I try to make the sugars in my kid's diet be mostly from fruit and I don't mean the "fruit snacks" sold in every shape under the sun. Fruit strips that are made only with chopped fruit, Lara Bars (ground nuts + fruit) make a great treat and have much more nutrition.
When my son does have candy I have found that chocolate has much less of a sugar rush.
We do desserts very rarely. If you keep dessert in the menu make homemade carrot cake cupcakes with cream cheese frosting so at least you control the ingredients and it has a little nutritional value. Or the all-fruit popsicles (check for added dyes or make your own). The choices for drinks in our house are milk, water, or the juice made by Naked or Odwalla that is just pureed fruit with no sugar or dyes. And because the juice is relatively expensive, we all limit our intake to make it last more days. We NEVER have juice drinks, soda pop, or energy drinks in the house. We carry reusable water bottles whenever we leave the house.
Start reading labels...you will be surprised the things that have dye added to them (some pancake mixes for example!)
Snacks: string cheese, plain yogurt with a little jam, or vanilla yogurt with fresh fruit chopped up in it, whole grain crackers with cheese and/or deli ham, carrot sticks with peanut butter, celery sticks with peanut butter/raisins (note natural peanut butter does not usually have sugar added), a vegie tray with favorites (cherry tomatoes, carrots, jicama, and whatever else your particular kids will eat).
My son and I are going to visit an Asian market next weekend so he can pick out some different exotic fruits/vegies to try.
When your kids start begging for a particular food in the store ask them to read the ingredient list. If there are words they can't pronounce say NO; if there is artificial dye say NO; if sugar, high fructose corn syrup, or the hundred other names for sugar are in the 1st 3 ingredients say NO. That is a good start. Challenge them to find new things that meet the new requirements.
I see a lot of parents make the mistake of not changing their own diet. They say no to the kids but the parent still keeps a cache of their own cravings foods/drinks. If you don't want your kids to eat/drink it, don't have it in the house!
Sugar is addictive. So withdrawal can be hard...