The answer to this question is rather surprising; Sanath Jayasuriya of Sri Lanka has been sent packing to the pavilion a record 34 times in ODI's without a run to his name, which is ironic considering he is one of the best limited overs batsmen of his geneation. He is followed by Wasim Akram on 28, who leads a group of four on 25 ODI ducks (Muttiah Muralitheran, Shahid Afridi, Mahela Jayawardene and Chaminda Vaas).
Below is the list in order of countries who have scored the highest amount of ducks with one player (number of ducks in brackets, country in bold, player in italics):
Sri Lanka - Sanath Jayasuriya (34)
Pakistan - Wasim Akram (28)
South Africa - Herschelle Gibbs (22)
New Zealand - Daniel Vettori (22)
West Indies - Chris Gayle (21)
India - Sachin Tendulkar (20)
Australia - Ricky Ponting / Adam Gilchrist (19 each)
Zimbabwe - Grant Flower (18)
Bangladesh - Habibul Bashar (18)
England - Alec Stuart / Marcus Trescothick (13 each)
Kenya - Stepen Tikolo (13)
Canada - Henry Osinde (7)
Scotland - Navdeep Poonia (7)
Netherlands - Bastiaan Zuiderant (7)
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Sachin Tendulkar has scored a total of 20 ducks in One-Day Internationals.
Notably, his first two One-Day international appearances ended in ducks - and his list of ducks includes three in three consecutive appearances in September-October 1994.