Psychology

The National Institutes of Mental Health from the National Institute of Health has a listing of statistics and other information.
The Mental Health Statistics list from the CDC is a list of statistical information and tests sorted by subject.
Fastats from the CDC is a list of quick, current statistics and related information regarding metal health.

Lists of data sets:

• An American Psychological Association list of links to data sets and repositories.
• The American College and Research Libraries list of links to available data sets.
• The Registry of Research Data Repositories has a searchable list of accessible data sets. 
• The Kinsey Institute Data Archive at the University of Indiana is a list of links to databases regarding human sexuality, health and public opinion.
• The Substance Abuse and Mental Health Services Administration has a list of data sets about mental health care.

Specific data sets:

• NHANES:  National Health and Nutrition Examination Survey from the Centers for Disease Control and Prevention (CDC).  Includes questionnaires, datasets and related documentation.
• NHIS: National Health Interview Survey from the CDC.  Includes questionnaires, datasets and related documentation.
• ADD-Health:  The national longitudinal study of adolescent to adult health hosted at the University of North Carolina. 
• NIF:  The Neuroscience Information Framework is an offshoot of the National Institutes of Health.
• SAMHDA:  Substance Abuse and Mental Health Data Archive (SAMHDA) is searchable on the ICPSR database hosted by the University of Michigan.
• The Clinical Trials is a registry and results database from the National Institutes of Health.
• Data.gov has a lot of different types of datasets, including some that are helpful for Psychology.

https://www.apa.org/research-practice/conduct-research/data-links