The following records require your permission before an employer can access them. Keep in mind, though, you may be asked to provide them.
Education records. Transcripts and discipline records are confidential. However, a school may release directory information to anyone. This includes your name, address, and degrees earned at their institution.
Military service records. Can only be released under special conditions and with your written permission. As with education records, however, some basic information is available by the asking, from your full name to the rank you held, the salary you were paid (if any), and your duty status.
Medical records. In many states, but not all, medical records are confidential. Very few circumstances guarantee an employer will ever have access to your medical history. One exception is if the company requires physical examinations from prospective employees, which will then give them implied access to the results.
Any information that could be used as base for discrimination (age, marital status, religion) is also confidential. Employers are not allowed to ask questions related to this in interviews.