Here are some websites that have available data sets.
MIMIC II PhysioNet
www.kdnuggets.com/datasets/
www.keel.es/
archive.ics.uci.edu/ml/
www.quora.com/Where-can-I-find-large-datasets-open-to-the-public
www.1000genomes.org
The Cancer Genome Atlas
Human Genome Browser Gateway
http://www.data.gov/
National Health and Nutrition Examination Survey
National Longitudinal Mortality Study
UCR Time Series Classification Archive
Yahoo News Feed Dataset
Clinical Practice Research Datalink
Time Series Data Library
Ohsumed and Reuters Classification Datasets
Biomedical Corpora in Stav
HCUP Nationwide Inpatient Sample
General Social Survey Data Explorer
CityPulse Smart City Datasets
Ann Arbor Electrogram Library