An international registry of data repositories, aka, a "database of databases." User-friendly browse and search functions make this an excellent resource for zeroing in on datasets of interest.
This site, maintained by Simmons College, lists a wide range of open access databases, organized by discipline. Make sure you scroll down to their Multidisciplinary Repositories list for more options.
An excellent source for public health data from the Centers for Disease Control and Prevention. Searchable by keywords, as well as browsable by topic and A-Z index.