I don't know why (maybe it's on a lesson plan for schools around the country) but this little question with a quick answer (and one that is quickly found in any ready reference) has been asked of me so often that I finally decided to list the answer here.
The answer is John Adams (second President) and Thomas Jefferson (third President). These two men died on the same day. But that's not all; read on....
The question with an even more interesting answer is, "On which day did they die?"
Both Adams and Jefferson died on July 4, 1826. The fiftieth anniversary of the signing of the Declaration of Independence. As we all know, Thomas Jefferson drafted the Declaration in committee with John Adams (and Benjamin Franklin).
After George Washington retired from the Presidency, John Adams became President and Thomas Jefferson became Vice-President. The two men had disagreed politically throughout the Washington Administration, and were only both elected because in those days, whomever came in second in the Presidential vote became Vice-President. During the Adams Administration, the two differed on almost every issue, and Jefferson defeated Adams and took the Presidency in 1800. To make a long story short, although they had worked together in the cause for independence, Adams and Jefferson became truly bitter enemies when political parties began to form around each of them.
Luckily, Adams and Jefferson reconciled in their retirement and they became the absolute best of friends as they lived out their final years. Both men were conscious of living to see the fiftieth Fourth of July, and both, despite knowing they were on their death beds, made genuine efforts to hang on to dear life until the day had come.
John Adams's final words were (supposedly), "Thomas Jefferson survives." But he was wrong. Jefferson had died just hours earlier at Monticello.
Five years to the day after Adams and Jefferson died -- on July 4, 1831 -- the fifth President, James Monroe, passed away. So three presidents have died on the same date: July 4th.
One more Presidential fact about the Fourth of July. Calvin Coolidge, the 30th President, was born in Vermont on July 4th, 1872!
In addition to the trio of Adams, Jefferson, and Monrow, there is another pair of Presidents who died on the same date: Harry Truman and Gerald Ford both died on December 26 (Boxing Day), Truman in 1972 and Ford in 2006.