U.S. unemployment figures are published monthly by the Bureau of Labor Statistics. The BLS posts a database of national unemployment data covering 1948 to the present. More detailed information is available in the Labor Force Statistics tables.
To find out the current unemployment rate in a particular U.S. state or city, you can go straight to the Economy At A Glance page of the BLS web site. For more information, see the Local Area Unemployment Statistics.
You can find more national, and state-specific and international data by following the "Unemployment" link in the left navigation column of the Overview of BLS Statistics page. Unemployment data is also published, along with other economic indicators, in Barron's and other business journals.