Electroencephalogram monitoring devices and online data repositories hold large amounts of data from individuals participating in research and medical studies without direct reference to personal identifiers. This paper explores what types of personal and health information have been detected and classified within task-free EEG data. Additionally, we investigate key characteristics of the collected resting-state and sleep data, in order to determine the privacy risks involved with openly available EEG data. We used Google Scholar, Web of Science and searched relevant journals to find studies which classified or detected the presence of various disorders and personal information in resting state and sleep EEG. Only English full-text peer-reviewed journal articles or conference papers about classifying the presence of medical disorders between individuals were included. A quality analysis carried out by 3 reviewers determined general paper quality based on specified evaluation criteria. In resting state EEG, various disorders including Autism Spectrum Disorder, Parkinson's disease, and alcohol use disorder have been classified with high classification accuracy, often requiring only 5 mins of data or less. Sleep EEG tends to hold classifiable information about sleep disorders such as sleep apnea, insomnia, and REM sleep disorder, but usually involve longer recordings or data from multiple sleep stages. Many classification methods are still developing but even today, access to a person's EEG can reveal sensitive personal health information. With an increasing ability of machine learning methods to re-identify individuals from their EEG data, this review demonstrates the importance of anonymization, and the development of improved tools for keeping study participants and medical EEG users' privacy safe.