This page contains a growing list of resoures to find information like federal and state school demographics, reports on achievement and attainment rates, employment stats for workers split by race and ethnicity, etc, etc. We're still trying to figure out how to best sort these on this page, so suggestions are welcome.
National Center for Education Statistics (http://nces.ed.gov/)
The NCES is the primary Federal entity for collecting and analyzing data about US education. Includes data on early childhood, K-16, postgraduate and adult education for everything from achievement and attainment to school safety, student debt, adult literacy, and issues related to teachers, such as career paths, employment rates and job satisfaction. Usually the best place to start when looking for nationwide statistics on anything related to education.
US Bureau of Labor Statistics (http://www.bls.gov/)
The Bureau of Labor Statistics of the U.S. Department of Labor is the principal Federal agency responsible for measuring labor market activity, working conditions, and price changes in the economy. Its mission is to collect, analyze, and disseminate essential economic information. Includes data on employment rates, wages, etc split by race, gender, and type of industry.
US Census Bureau (http://www.census.gov/)
Particularly useful sections on the Census Bureau page are Data and People. The first includes all the statistics you might expect from the Census, while the second lists papers published by the bureau, sorted by subject/category.
US Bureau of Justice Statistics (http://www.bjs.gov/)
Statistics on incarceration and crime rates by education levels, race/ethnicity and gender.
State Demographics and Statistics
The following sites include demographics and statistics reported by the states. Generally they cover K-12 public education aggregated by school, district, county and state. Information typically includes (but is not restricted to) attainment and achievement rates, student demographics, including gender, race, socioeconomic status (as measured by enrollment in the Free and Reduced Price Lunch Program) and English Language Learners, and staff and teacher demographics.
Arizona (http://www.azed.gov/): This site is rough to navigate, but check under Accountability >> Research & Evaluation for dropout and graduation rates, and under School Reports / School Results >> State Report Card for most other demographic info, including breakdowns of achievement by race and gender.