There are two reasons why JS Mill might exempt children from the harm principle.
One is that children should not exercise their liberty to their own detriment, even when they would be allowed to if they were adults because nobody else would be harmed.
But a different reason is that children do not possess liberty at all, so that it would be impossible for the harm principle to apply to them even if we wanted it to.
Could this be Mill's real reason? I think so.
Allow me to quote Mill's entire paragraph about children that was partially quoted by John Perry above:
It is, perhaps, hardly necessary to say that this doctrine is meant to apply only to human beings in the maturity of their faculties. We are not speaking of children, or of young persons below the age which the law may fix as that of manhood or womanhood. Those who are still in a state to require being taken care of by others, must be protected against their own actions as well as against external injury. For the same reason, we may leave out of consideration those backward states of society in which the race itself may be considered as in its nonage. The early difficulties in the way of spontaneous progress are so great, that there is seldom any choice of means for overcoming them; and a ruler full of the spirit of improvement is warranted in the use of any expedients that will attain an end, perhaps otherwise unattainable. Despotism is a legitimate mode of government in dealing with barbarians, provided the end be their improvement, and the means justified by actually effecting that end. Liberty, as a principle, has no application to any state of things anterior to the time when mankind have become capable of being improved by free and equal discussion. Until then, there is nothing for them but implicit obedience to an Akbar or a Charlemagne, if they are so fortunate as to find one. But as soon as mankind have attained the capacity of being guided to their own improvement by conviction or persuasion (a period long since reached in all nations with whom we need here concern ourselves), compulsion, either in the direct form or in that of pains and penalties for non-compliance, is no longer admissible as a means to their own good, and justifiable only for the security of others.
Now, obviously Mill is not talking about children per se, but rather about people who are not "in the maturity of their faculties." Mill writes that not only children, but also "those backward states of society in which the race itself may be considered as in its nonage," are exempt from the harm principle, and "for the same reason." The reason is not that they possess liberty which must be restricted, but rather that they do not possess liberty at all. "Liberty, as a principle, has no application to any state of things anterior to the time when mankind have become capable of being improved by free and equal discussion."
By the way, let me be clear that I very strongly disagree with Mill's racism, as I'm sure we all do.
In any case, Mill gives the same rationale for parenting children as for colonial imperialism: one is a benign despot/parent whose ultimate aim is to provide one's subjects/children with their own eventual liberty, of which they have none yet.
So the question for Mill is not how the liberty of children should be restricted. That's a loaded question which must be rejected because it assumes that children have liberty when in fact they do not. Rather, the question is how the liberty of children should be ACQUIRED. For the harm principle will not apply to them until they first have liberty to restrict, and they will not have liberty at all until they "have become capable of being improved by free and equal discussion."
Therefore, according to Mill, nobody possesses liberty by necessity, or by nature, but only as a matter of contingency, by nurture. Liberty is a skill which must be acquired, developed, nurtured. And like most skills, liberty could remain unacquired one's entire life if left undeveloped. Hence the intimate connection between education and liberty, and thus education and children.
Liberty, according to Mill's European intellectual tradition, is a power or capacity developed by means of education in the liberal arts, of which traditionally there were seven: grammar, logic, and rhetoric constituted a basic primary education, while arithmetic, geometry, and applied mathematics like harmonics and astronomy constituted a more advanced secondary education. Acquisition of these basic skills or "arts" was considered necessary in order to possess liberty. The idea was that in order to make genuinely good choices in life, and thus be genuinely free, one must be able to read, write, make and evaluate arguments, do basic arithmetic and deliberate with others -- or as Mill puts it, "become capable of being improved by free and equal discussion."
Now, I wish to make one suggestion: that in order for children -- or anybody else, for that matter -- to become capable of being improved by free and equal discussion, they must be taught how to engage in free and equal discussion in the first place. How many parents teach this to their children as a skill? On the contrary, many parents deny their children free and equal status in discussion! And if there is no free and equal discussion between parent and child, how can parents teach their children this valuable skill?
Philosophy is in many ways ideally suited to teach children of sufficient cognitive development the skill of free and equal discussion. Philosophy is typically not about practical concerns which could get children in trouble, but rather about hypothetical or theoretical questions that can train children's minds without endangering their bodies. Philosophy provides that practice without risk of children making bad choices on practical matters which may cause harm.
So parents, grab your Plato and start practising some dialectic, because you've got discussion with your children as free equals to attend to....
Cheers,
-paul

As a mother of 3 young children I have come up against these issues and had to develop my own philosophy. Most of the time I manage to abide by it but I admit at times I resort back to "because I said so" only because in that moment I am lacking patience. However, I do beleive that children must decide what is right and wrong on their own and no amount of me telling them will pursuade them unless they reach there own conclusions from personal experience. Personal experience sticks better in the memory. When using force or fear to control a child you are only creating another struggle within themselves and with the world around them. People tend not to think you can pursuade or reason with a small child but at 1 year of age I found patient explination was far more effective. If I can give them a good enough reason that makes sense in their perspective then they will go along but if I use force then I only get struggle and fighting. As the get older they need solid logic and reasoning so that they can talk themselves through situations that are challenging. However if it is force and fear that has been emebedded in their minds then as they get older they will only find loopholes to get around it. This forces children to lie and do things in secret so that they can get away with it. And if no one is around to rule them by fear then what will they rely on in the long run to stay out of trouble?
I truly beleive that if we expect our children to be responsible, compassionate and understanding adults then we must instill a solid reasoning process in their minds and help them overcome stuggles by using their minds and not their emotions. Better yet, we should teach them to integrate the two so that they have a double check system through the decision making process.

I agree with Mill, I think it's easier to see a connection to liberty if Adulthood is a measure of Maturity and not just age, then the immature would not necessarily be children but anyone who continues to do harm to himself and others out of either self gratification or ignorance. The problem seems to arise with accountability, for example - if children crave attention they will do anything and everything to gain it - which means experimentation, they don't understand their actions because they don't have a broad enough set of experiences from which to judge the consequences. So without being given the proper attention they cannot be held accountable; instead the accountability is passed on to the parents, and so the Child's sovereignity doesn't really exsist.
This part: "But what about all of those who make it to adulthood without developing such habits, skills and knowledge? " we know what happens - we see them at the supermarket pushing carts, or on the street asking for change, or in prison, on court TV, the Jerry Springer show, or in the Hospital.
My question would be "At what point does a person stop being a product of their environment and at what point does the environment become a product of the person in it" I think that point where that happens is the dividing line between the child and the adult

If you're interested in these questions you might appreciate this famous PBS Frontline documentary:
http://www.pbs.org/wgbh/pages/frontline/shows/divided/etc/view.html
Cheers,
-paul

That Tamar Shapiro is pretty cute.