Being from Tennessee I know we have gone in the winners column 21 of the last 23 elections, so I feel it is a good bellweather state. The only times it hasn't been carried by the winner since Williams Jennings Bryan last carried it was 1924 (John Davis) and 1960 (Richard Nixon). I felt is was under stated in 2000 that if Al Gore had carried his home state of TN it wouldn't have matted who carried Florida, he would be President. I know in the past some candidates have not carried their home state but usually in an election where they were whipped badly (i.e., McGovern, Alf Landon). I don't think there is any other time when the home state denied the favorite son the presidency.
On the subject of carried the least, I would have guessed maybe Mississippi too. Both my parents were born there, and I always found it bizzare that in 3 out of 6 elections (1948 to 1968) Mississippi went for neither the Republican or Democrat. That is about as far out in the political wilderness as a state can get.
Two other trivia notes about Tennessee; in the five Presidential elections where Whigs got electoral votes (1836-1852) Tennessee went for the Whigs every time, along with Kentucky and Vermont. I don't know why they were such a bastion of Whigism. Also, Tennesse was the first state to break with the Solid South, in 1920, going for Harding. It was the first time since Reconstruction, 10 straight elections, that all eleven confederate states did not go Democratic.
Actually, in 1888, Cleveland lost his home state of New York, which if he had won it, would have won him the election. He also won the popular vote and lost the electoral, so there was quite a bit of symmetry between Cleveland and Gore.
Another person similar to Gore in this regard is James Polk, who, like Gore, was from Tennessee and won the nationwide popular vote, but lost Tennessee.