In my discussion of the economics underlying the reason for the mandate (and the penalties needed to enforce it), I talked about the adverse selection problem, but I wish I would have talked about moral hazard as well since that is also part of the problem.
Under adverse selection, relatively healthy people drop out of insurance pools because they expect their health costs to be less than they would have to pay for insurance. As the relatively healthy people drop out, it raises the average cost of covering people (since the relatively healthy are no longer in the pool), which causes more people to drop out (the ones with expected costs that are now less than the higher premiums), which raises the price again, which causes more people to drop out, and so on until the market breaks down entirely.
But even healthy people have some chance of catastrophic illness, illness that could be deathly for example, so why wouldn't they purchase insurance in case this happens?
People know we are a compassionate society, and if they come down with a life threatening disease we will take care of them even if they don't have insurance, i.e. even if moral hazard causes them to shirk the personal responsibility conservatives hold so dear. Thus, relatively healthy people can take a chance and go without insurance secure in the knowledge that they will be treated if something awful happens. Broken bones, catastrophic illness and so on will be covered. But covered by whom? In many cases, the individual will not have sufficient resources to pay for the medical care, it would bankrupt them, so there is no choice but for all of the rest of us to pick up the bill.
A mandate stops this from happening. It forces those who would take a chance and go without care, those who are relying on all of the rest of us to insure them against large, unavoidable medical costs, to insure themselves against this. That is, it stops this moral hazard behavior. (Essentially, adverse selection is about the average or mean cost, moral hazard is about the variance -- loss of life, for example, can be viewed as a very bad draw that occurs with some probability and imposes very large, perhaps infinite costs.)
Adverse selection and moral hazard are not mutually exclusive. As you can see, they work together -- people with expected costs lower than premiums drop out knowing they are covered by the rest of us against a bad draw. A mandate, or its equivalent, helps to overcome both of these problems.