This page is merely a greatest hits of federal data sets. There are hundreds of thousands of publicly available datasets from the federal government. If you don't see what you need here, ask a librarian to help you!
The CIA World Factbook is a wealth of information collected by the CIA about countries around the world. The datasets are wide ranging including Geography, People and Society, Government, Economy, Energy, Communications, Transportation, Military and Transnational Issues. Each of these topics is followed by dozens of subtopics. You can examine the topic and view all the countries listed (people and socieity -> birth rate -> list of contries), OR you can select a country and examine all the information about the country. There are also detailed country and regional maps.
Data.gov is a one stop shop for federal data. There are literally hundreds of thousands of datasets to choose from. The easiest way to deal with this data is to select the topic from the choices on the first page, and then refine from there. For example, if you select Public Safety, the click data from the menu bar, you get 74 possible datasets on topics like food recalls, campus safety, or weather emergencies, to name a few.
Healthdata.gov is the federal government's clearing house for all data related to health. It includes information from the National Institutes of Health (NIH), the Food and Drug Administration (FDA), the Centers for Disease Control (CDC), and many others. This site also includes data from states which have been reported back to the government. For example, a report on lead in school drinking water submitted by the state of NY.
Note - many of these items are raw datasets which can be viewed in an excel table. You may need to do some analysis yourself to examine this data. Perfect for someone who is taking statistics!
The US Census Bureau collects data on housing, economics, education, population and many other topics. This site includes tools for data visualization and you can break it down by zip code and neighborhood. It is easy to get lost examining all the information on this site!