Whyyyyyy won't my kids stop whiiiiiiining? The reality of it is that they are just in one of those phases. Julie Tilsner wrote an article on CNN's parenting.com about why our kids whine and how we can stop it.
With toddlers, a lot of the time they don't even know they are whining, they do it because they have trouble communicating. The article suggests letting them know how they sound and either snuggling or giving the child a snack to make them happy.
Preschoolers (this is my problem) whine because they are going through so many changes and they don't always know how to express being overwhelmed. Help them by reminding them to use a polite tone of voice or have them "pour the whine" into a bowl or cup.
In grade school the kids whine because they are tired, hungry, bored or don't want to do what you are asking. A fitting solution is sending them to a "whine room" where they can vent their frustrations, but you don't have to listen to the whining.