The most influental U.S. presidential loser of the 20th Century?

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Out of the major parties, eventually strong third parties, nominees (thus, not counting loser for a nomination).

I'd say Barry Goldwater.

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Goldwater, while losing badly, with him winning a nomination ended the a longtime domination of people like Dewey and Rockefeller within the Republican Party, changed Republican strategy by aiming on the Dixie.

Yes, despite losing his presidential bid was most influental in a historical perspective.

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FDR was not a "presidential loser". He was a "vice presidential loser", ftr.

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Hoover.

How was Hoover at all influential after 1932? The Republican Party even abandoned his conservative foreign policy and adopted FDR's internationalism. Robert Taft could not once get nominated.

Hoover managed to singlehandedly ruin America, and the effects of his ruination continue to be felt today.

Single-handedly ruin? Andrew Mellon, several senators, and the entire Federal Reserve (biggest culprit) certainly had a rather large hand in it themselves.

Hoover just get the entire s**t hitting the air. While he indeed was a clumsy in dealing with depression, he's not the one responsible for collapse. Such things are long running processes with a deeper roots.