Six is the most current or former presidents who have ever been alive at the same time, but this isn't the first time it's happened. There have been three other periods when six were alive simultaneously:

• 1861, after the inauguration of Abraham Lincoln: former presidents James Buchanan, Franklin Pierce, Millard Fillmore, John Tyler and Martin Van Buren were all still alive. This streak ended with Tyler's death in January 1862.
• 1993, after the inauguration of Bill Clinton: former presidents George H.W. Bush, Ronald Reagan, Jimmy Carter, Gerald Ford and Richard Nixon. Ended with Nixon's death in April 1994.
• 2001, after the inauguration of George W. Bush: former presidents Clinton, Bush, Reagan, Carter and Ford. Ended with Reagan's death in June 2004.

Wikipedia has a great graph mapping the lifespans and terms in office of all presidents. It basically reflects broad demographic trends over the past 200 or so years: people being elected president at younger ages, and living longer generally. Jimmy Carter holds the current record for longest presidential retirement: it's now more than 36 years since he left office. The previous record holder was Herbert Hoover, who lived another 31 years after leaving office in 1933.

(At the other end of that spectrum is poor James Polk, who died a little more than three months after leaving office, making him the president with the shortest retirement — not including the eight who died in office, obviously...)