"Corruption is a national sport every day at the direction of customs officials," said Cherif Mohamed Haidara, who heads a group of businessmen.
Medical treatment was the second most common reason cited after paying off officials to obtain a document or permit, said Richard Houessou, who headed the Afrobarometer project in French-speaking Africa.
The problem of medical bribes was the worst in Uganda reported by 46 percent of respondents. Swaziland at 41 percent and Niger with 40 percent were close behind.
"Among the poorest those who went without food at least once in the past year 18 percent had to pay a bribe at least once in the previous year to receive treatment, compared to a substantially lower 12 percent among those who were better off," the report found.
The survey also found that more than half of the people polled were dissatisfied with their governments' efforts to battle corruption.
Nigerians gave the worst ratings to their government on its efforts to battle graft, with 82 percent saying the government was doing fairly badly or very badly.
Pollsters with the Afrobarometer project conducted 51,000 face-to-face interviews across Africa between October 2011 and June 2013. Afrobarometer selected 34 countries of the more than 50 on the continent to survey, but did not include many in Central Africa, leaving out Congo, Chad, Central African Republic and Gabon.
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Associated Press writers Boubacar Diallo in Conakry, Guinea and Clarence Roy-Macaulay in Freetown, Sierra Leone contributed to this report.
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Follow Krista Larson on Twitter at https://twitter.com/klarsonafrica.