As the U.S. government shutdown drags on, its impact on government-provided data sources ought to give IT admins and developers a case study to reflect on for a long time to come.
But in the short run, a lot of government-provided data sets -- used by businesses, nonprofits, individuals, and governments alike -- are not being updated or are completely unavailable.
The United States normally maintains a broad list of data APIs through its Data.gov site, many of which are echoed in ProgrammableWeb.com's list of government-supplied APIs. Unfortunately, even the Data.gov lists are offline (try the Internet Archive for a backup copy of the master list).
Here's some of the most relevant and useful APIs and data sources that are offline for the time being, along with some suggested backups.
Government APIs that aren't working
Bureau of Economic Analysis: Even historical data isn't available right now from the BEA; the entire site has gone dark.
Bureau of Labor Statistics: The agency normally responsible for issuing jobs reports will "not collect data, issue reports, or respond to public inquiries" during the shutdown period. That means no data on job losses or gains, and no unemployment numbers (all of which were scheduled to come out this Friday).
Census Bureau: As with the BEA, the Census Bureau is totally dark. However, others have suggested the state-level Missouri Census Data Center as an interim alternative, since it has historical data for all states, not just Missouri.
Centers for Disease Control/National Center for Health Statistics: The CDC's Content Syndication section still appears to be online, although with the disclaimer that it may not be updated, likewise the Health Indicators Warehouse. WONDER (mortality data) is totally offline, including historical data.