After the 1995-'96 government shutdown, the Congressional Research Service detailed (PDF) how many employees at different agencies had been furloughed. The employees who were "excepted" from furlough would now be considered "essential" federal employees.
Some background from the CRS report:
The longest partial shutdown of the federal government began on December 16, 1995, furloughed an estimated 260,000 federal employees, and ended on January 6, 1996, after the White House and Congress agreed on a new resolution to fund the government through January 26, 1996. It was the second shutdown in 1995-1996. On January 2,1996, the estimate of furloughed federal employees increased to 284,000. Another 475,000 federal employees, rated "essential," continued to work in a "non-pay" status.
Some hard-line conservative will inevitably champion the government shutdown as laying bare the issue of government waste. But going by the chart above (which compares the CRS data with the 2013 numbers the OMB has released so far), it shows federal workers' shrinking "essentiality" over the past 17 years. In 1996, the Department of Commerce defined 40 percent of its employees as essential; now, Commerce is projecting that just 13 percent of its employees will keep working during the shutdown. Only the Department of Veterans Affairs, the Smithsonian Institute, and the Environmental Protection Agency will keep a larger proportion of workers around during the shutdown than they did in 1995.
It's important to keep in mind this chart measures the percentage of federal workers defined as essential, not the raw numbers, so it's not perfectly scalable. For example, there are almost twice as many "essential" VA workers as employees at the other agencies on the graph combined. (The NYT also has a nice graphic breaking down who will and won't be going to work tomorrow.)
This isn't a comprehensive list of agencies, for a variety of reasons. Some agencies, like Homeland Security, didn't exist in 1996. Others were incorporated piecemeal into new agencies. And not all agencies have said exactly how many of their workers will be furloughed tomorrow. But now is clearly the time to prep your best jokes about how the events of Gravity are due to a lack of NASA personnel.