Free Data Sets
Bureau of Labor Statistics
Many important economic indicators for the United States (like unemployment and inflation) can be found. Most of the data can be divided both by time and by geography.
The Centers for Disease Control and Prevention maintains a database on cause of death. The data can be segmented in almost every way imaginable: age, race, year, and so on.
U.S. government data, this site acts as a portal to all sorts of amazing information on everything from climate to crime.
DataCite
Search for datasets across over 1000 different major data centers and repositories including ICPSR, Harvard Dataverse, Data-Planet, etc.
One key differentiator of data.world is the tools they have built to make working with data easier - you can write SQL queries within their interface to explore data and join multiple data sets. They also have SDK's for R an python to make it easier to acquire and work with data in your tool of choice.
FBI Crime Data
National crime statistics, with free data available at national, state and county level.
HealthData.gov
US healthcare data including claim-level Medicare data, epidemiology and population statistics.
Pew Research Center Datasets
Raw data from Pew's research into American life.
Datasets covering population demographics and a huge number of economic and development indicators from across the world.
World Health Organization - Data and Statistics
Offers world hunger, health, and disease statistics.