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."