Google Dataset Search lets you find datasets hosted in data repositories only. Searching here first is a good choice when looking for data that might be hosted in a repository. This covers most of the repositories listed on this page.
From Web of Science. Discover datasets from multiple repositories in one place. The Data Citation Index provides digital research that is discoverable, citable and linked to primary research literature. [Make sure Data Citation Index is selected from the pulldown.]
The goal of re3data is to create a global registry of research data repositories. It covers research data repositories from different academic disciplines for the permanent storage and access to datasets. It also aims to promote a culture of sharing, increased access and better visibility of research data.
The Inter-university Consortium for Political and Social Research (ICPSR) provides a vast archive of social science data for research and instruction. Users may view documentation, download raw data, and search a bibliography of data-related literature. (You must create a personal ICPSR account in order to download data.)
Dryad is a curated general-purpose repository that makes the data underlying scientific publications discoverable, freely reusable, and citable. Dryad has integrated data submission for a growing list of journals.