A visit to the doctor may be covered, only to discover that the prescription she wrote is not. Even if the medication is being widely prescribed for your particular condition, the insurance company may have other procedures, or prefer that you are treated using a different medication. The only recourse in a situation like this would be to have a secondary insurance plan that pays for your prescriptions, but even then you could run into the same type of problem if a generic medication is available in place of the one prescribed.
The health insurance industry should be thought of as a business. As such, your policy is written to give you the most comprehensive medical coverage available within the scope and budget of the plan. If a generic version works just as well, the insurance company will prefer you to use the generic in order to cut costs.
In some cases, the medication you were prescribed is either not recognized or not yet approved by your health insurance plan. For example, your doctor might prescribe Xanax for an anxiety problem, but the insurance company will only pay for generic equivalents. You are still able to get the same treatment using a generic form of the medication, and the insurance company is able to reduce costs by supplying you with an alternative to the name brand.
In other cases, the health insurance company is required to cover a procedure, but not the medications or supplies needed after the procedure is complete. This situation differs from the previous one because there is no generic equivalent being offered. If this happens, your choices are to either appeal the denial or pay for the medication using cash or an alternative insurance plan.
Another situation which could arise would be if your prescriptions have not been researched by the insurance company. Medical advances are happening very quickly in the modern world, and it is quite possible that you could be written a prescription for a product which the insurance company has not yet evaluated. You will either have to pay for the prescription yourself or talk to your doctor about using medications which have already been approved by the insurance plan.