1956 and 1996 are obvious choices. In a few more years, I think one could add 2004 and 2012 to the list.
Comparing only 1956, 1972, 1984, 1996, 2004, 2012: I think 2004 was the most interesting and the most diferent in this family. Reelections are usually boring. But 2004 was not. The turnout was high. Much bigger than 1996. It was the first presidential election after the 9/11, so the international media and international public opinion was much more interested in the 2004 election than they were in 2000 (there was big interest in the 2000 election by international media and international public opinion only after the polls were closed, not during the campaign). Usually, the public outside the US is divided. In 2004, it was the first time when almost all the international media and the international public opinion supported the same candidate. This situation repeated in 2008 and 2012. Other innovation brought by 2004 was internet campaigning, the use of social networks.
1972 was also somehow interesting because of the looser, and not because of the winner.
1984, I donīt know why, it very remembered in this forum.
About 1956 and 1996, I don't know what to say. And I don't know what people will talk in 2030 about 2012.