It is becoming more common practice to deposit data into repositories, which "are a centralized place to hold data, share data publicly, and organize data in a logical manner" (Harvard Medical School Data Repositories).
Data repositories can be disciplinary, interdisciplinary, and/or hosted by specific institutions.
Examples are provided of each of the above designations, but the Data Repositories to Store, Share, and Search for Data section of the Data Management @ ODU guide includes additional information about data repositories in which to search for data.
Disciplinary repositories, also called domain-specific, are focused on a particular field of study or data type.
Interdisciplinary repositories, also called generalist repositories, accept data from all disciplines, in many formats. These repositories can be used when there isn't an appropriate, or required, domain-specific repository.
Institutional repositories are hosted by a specific institution, and can often only be used by affiliated members. Harvard Dataverse is an exception in that anyone can deposit data.