In general, very few people have a right to see a patient's medical history or files. The doctor-patient privilege is a sacred one, but also with some teeth behind it. The Health Insurance Portability and Accountability Act (HIPAA) has a privacy clause which requires that companies or organizations with medical histories take reasonable steps to ensure that data is kept private and secure. It also requires that permission must be obtained to release records to third parties.
This would include insurance companies, and often patients must sign permission forms for release of records before insurance companies will pay on claims activity.
In addition, medical information could be released to relatives either with a patient's consent, or if they have power of attorney or guardianship of the patient which empowers them to make medical decisions for them. This would of course include minors in the care of an adult, or the elderly who have given legal control of their decisions over to a relative. In rare cases, a court order or subpoena might require medical records to be released.