Interesting question, but literally only one other president was even alive during the Great Depression - Herbert Hoover. William Howard Taft died in 1930. Hoover was only 58 when he left office and he lived until 1964 (meaning he would have seen an FDR, Truman, Eisenhower, Kennedy, and start of the Johnson administration)

The question is a pertinent one, however, since Hoover's reputation was almost completely destroyed by the Great Crash. Today, when we learn about Hoover it's usually in this context - he led us to the Depression, right? What most people forget is that Herbert Hoover was an international celebrity before taking office. In the wake of the terrible disaster of World War I, Hoover led the international efforts to combat famine in European countries. He became immensely popular.

When the economy tanks, Hoover takes some actions, but really doesn't do nearly enough to help turn the economy around. He says stupid things that get reprinted in the newspapers (the newspapers also print some stupid things he probably didn't even say at all).

Hoover remained connected to politics through the next several decades - he certainly didn't starve himself during the economic depression - but he mostly carried on behind the scenes. When a controversy or election came up, however, newspapers would turn to him as a former president for comment (not unlike today). He again became involved with combating international famine. He critiqued the administration's Cold War policies and the intervention in Korea.

Interesting guy, all in all.

Read either Herbert Hoover: The American Presidents Series: The 31st President, 1929-1933 or The Crusade Years, 1933–1955: Herbert Hoover's Lost Memoir of the New Deal Era and Its Aftermath.

More from a good source - http://millercenter.org/president/hoover/essays/biography/6