Banducci was born in 1922 in Bakersfield, California. He came to San Francisco at age 13 to study under the concertmaster of the San Francisco Symphony. He changed his first name to "Enrico" after Enrico Caruso. He was married five times, the first to Raimonde Verney, daughter of a symphony violinist. He wore a beret, beginning after a health inspector insisted he wear a hair covering while he was running a food operation and continuing to cover his eventual baldness. He bought the hungry i for $800 in borrowed money in 1948. Although he once calculated that he made over ten million dollars from his various projects, he spent it all. He spent time in jail, and was involved in a number of brawls. The hungry i went bankrupt at least once.
In 1981, Mort Sahl, Jonathan Winters, Irwin Corey, Jackie Vernon and a host of others gathered to film a tribute to Banducci that was nationally televised and called The hungry i Reunion. The film is intercut with reminiscences by Bill Cosby, Maya Angelou (who started at Banducci's club performing Caribbean songs and patter with a Caribbean accent) and Phyllis Diller.
In 1988, after he lost Enrico's to one of its several closures over the years, he became a hot dog vendor in Richmond, Virginia at the "hungry i hot dog stand", located on property he had purchased for his son years earlier in the city's most upscale restaurant district that he'd, before eventually moving back to San Francisco in the late 1990s.