World Data: Our World in Data
Open Government Data India - Data.gov.in
Census data: US Census data
Open data concept read more at Wikipedia
Kaggle: Data Science
ProPublica: Wide variety of data available for purchase. Some of the data include Medicare related data.
Bioinformatics and Science Data:
Reactome.org - open-source, open access, manually curated and peer-reviewed pathway database. Reactome relates human genes, proteins and other biomolecules to the biological pathways and processes in which they participate.
Imngs.com - Integrated Integrated Microbial Next Generation Sequencing (IMNGS).
HumanCellAtlas : A map of human cells.
HealthCare Analytics and Data
C-Path.org - The Critical Path Institute nonprofit organization to develop new evaluation tools and standards for drug therapy trial to help accelerate regulatory qualification and medical product approval and adoption.
Healthdata.org - The Institute for Health Metrics and Evaluation (IHME).
National (Nationwide) Inpatient Sample (NIS) - The NIS is the largest publicly available all-payer inpatient health care database in the United States, yielding national estimates of hospital inpatient stays.
DOPPS.org - Dialysis Outcomes and Practice Patterns Study Program. This site contains dialysis data and can work with external researchers for independent analysis. US and International data available.
National Health and Nutritional Examination Survey (NHANES) III data - ( *findinfoandlink*)
AHD.com - American Hospital Directory - information about US based hospital including fianancial data. (has both free and paid options)