We had "nearly" paid of the national debt in 1980. It was just below $800 billion at that point, after Truman began paying off WWII and the Great Depression:
Reagan: 1980 was 907B - added $2.1T, up 275% in 1988 to $3T
Bush I: 1988 was $3T - added $1.8T, up 63% in 1992 to $4.8T
Clinton: 1992 was $4.8T - added $1.2T, up 22% in 2000 to $6T
Bush II: 2000 was $5.1T - added $6.6T, up 129% in 2008 to $11.7T
Obama: 2008 was $11.7T - added $4.3T, up 37% in 2012 to $16T
Compiled directly from the numbers at the Dept. of the Treasury: http://www.treasurydirect.gov/govt/reports/pd/histdebt/histdebt.htm
But to answer the question directly, I guess the last President to pay off/reduce debt was Carter, though all of them since WWII had been doing it.