Vanderbilt University Government Statistics Website 
(NOTE:  This is not a government website)
Arranged by topic, this is a very easy to use, comprehensive site for finding government statistics. While not a government website, it includes links to many official government sources.

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Other Popular Sites:

American Factfinder Quick statistical facts on the U.S.

Bureau of Labor Statistics Useful economic data CPI, PPI, unemployment rate, etc. see "Economy at a Glance" on this site

FEDSTATS  A gateway to statistics from over 100 federal agencies

Statistical Almanac of the United States  Summary statistics on just about any topic (often for a range of years) - lacks detail to lower levels of geography (ie. counties, etc.) but is a good pointer to other sources.

USA Trade  (in library use only - ask for LOGIN help at the Research Help Desk )
“USA Trade Online is an online resource providing current and cumulative U.S. export and import data for over 18,000 export commodities and 24,000 import commodities.  USA Trade Online provides trade statistics using the Harmonized System (HS) up to the 10-digit level and the North American Industry Classification System (NAICS) commodity classification codes up to the 6-digit level.” (NOTE: STAT-USA is no longer with us)

USC - Data on the Run: Data & Statistical Sources for Reference & Instruction NEW!!

U.S. Census Bureau Population Statistics and demographic information, etc. from the U.S. Census Bureau (includes "American Factfinder")