As you probably know, when Bill Clinton left office, the budget was in surplus and both the White House and the Congressional Budget Office projected that the external U.S. debt would be completely repaid by about 2010. Instead, we're more than $12 trillion dollars worse off.
Update 2017 February 9 and April 20: This post was originally published in mid-2011. Since then the total national debt has continued to increase every year.
When spending exceeds what the government takes in in taxes and fees, we have a budget deficit. A deficit is covered with additional borrowing, so the deficit represents the amount of increase in the national debt.
The annual deficit fell during the Obama years from 9.8 percent of gross domestic product in fiscal 2009 to 3.2 percent in fiscal 2016. (See this interactive chart from the St Louis Fed.) But the deficit was higher in 2016 than in 2015, and based on current proposals from President Trump it is likely to increase further. See also this post about support for a growing deficit among many congressional Republicans.
The U.S. most recently ran a budget surplus -- and started paying down the national debt -- during the last years of the Clinton administration. George W Bush's tax cuts put an end to that, as noted below. The next most recent surplus budget was the final one passed under President Lyndon Johnson at the height of the War on Poverty, the War in Vietnam, and the Apollo Program.
Below is another chart that goes into more detail, listing not just deliberate policy changes but external factors, such as the recession. The source for this one is the Obama White House, but as far as I can tell the numbers are accurate, based on those published by the non-partisan Congressional Budget Office. What to do about it is a matter of political opinion, but hard facts are a useful starting place. (See also this accompanying explanatory page and this paper from the Pew Charitable Trusts.)
(Click on the chart above for a larger version.)
Update 2017 February 9: The White House page holding the graphic above has been deleted by the new administration, but the Obama-era website has been preserved by the National Archives here, and I have adjusted the "another chart" link above the graphic to point to the archival site.by