This page from the Social Security Administration's website gives links to various tables of data about Medicare, Social Security, Taxes, etc. Data files are available as pdf, html, or Excel files.
The datasets on this page are classified by analysis technique (ANOVA, Linear Regression, Markov Chain Monte Carlo, Nonlinear Regression, and Univariate Summary Statistics) and by level of difficulty (lower, average, higher). They were originally intended to test statistical software.
As quoted on the site, "The National Center for Catastrophic Sport Injury Research collects and disseminates death and permanent disability sports injury data that involve brain and/or spinal cord injuries." Links to data, annual reports, and definitions of injury are included.
This site offers links to a multitude of data tables in PDF format. Topics include national trends in injury hospitalizations, trends in health and aging, summary health statistics for the U.S. population, trends in health insurance and access to medical care for children under age 19 years, and many more.
This data archive contains data sets divided into the following categories: Astronomy, Biology, Education, Geography, Social Sciences, Sports, Transportation, Weather, and Miscellaneous. The datasets can be viewed as an html page or downloaded into Excel spreadsheets.
Each dataset in this collection includes description of the study, description of the data file, statistical topic covered, and reference. Topics addressed include: correlation, one-way ANOVA, Bonferroni multiple comparison procedure, regression (simple, multiple, and loglinear), chi-square, and the t-test.
The ICPSR provides access to a large repository of social science and political data. Data sets can be constructed and downloaded for use in most popular statistical packages.