Use the following sites to search for discipline-specific data repositories and standards:
PLOS recommended repositories - PLOS journal recommendations for general and discipline-specific data repositories.
Scientific Data recommended repositories - Recommendations for general and discipline-specific data repositories. Nature Publishing Group.
re3data - Registry of Research Data Repositories - "Re3data is a global registry of research data repositories that covers research data repositories from different academic disciplines"
NIH-supported data repositories. List maintained by the Trans-NIH BioMedical Informatics Coordinating Committee (BMIC).
FAIRSharing - "A curated, informative and educational resource on data and metadata standards, inter-related to databases and data policies"
OAD (Open Access Directory) Data Repositories - "The Open Access Directory (OAD) is a compendium of simple factual lists about open access (OA) to science and scholarship, maintained by the OA community at large."
Google Dataset Search enables users to find datasets stored across thousands of repositories on the Web, making these datasets universally accessible and useful.