Apologies if this breaks the 20 year rule, to my knowledge no recent presidents smoked, but I could be wrong. Edit: If any recent presidents do smoke, who was the most recent, prior to 1996.
The last president to smoke regularly was Ford, but Ford smoked a pipe. Carter was the consummate teetotaler and didn't smoke either. Reagan quit before he became President, but did smoke in his younger days; the elder Bush was, as far as I can tell, a non-smoker; Clinton also smoked, but only cigars; W. is said to have smoked cigarettes in the White House as is his wife, but those are rumors and no concrete evidence has come to light, and Obama has been public with his attempts to quit smoking cigarettes. Going a bit further back, Roosevelt was a well known smoker, Truman was a non-smoker, Eisenhower smoked, while Kennedy, Johnson, and Nixon were all cigar aficionados.
Interestingly, Johnson is said to have started smoking again on Inauguration Day 1969 (after having given up cigarettes after a heart attack some 15 years earlier), the day his successor Nixon was sworn in, proclaiming that since he had raised his children and been President, it was his time and he could do as he pleased.