The first opening of the TV anime, "We Are!", won the Animation Kobe Theme Song Award of the year 2000. In February 2001, One Piece placed 9th among TV anime in Japan. In 2001, the readers of Animage, a popular Japanese anime magazine, voted the TV anime in 5th place of "The Readers' Picks for the Anime that should be remembered in the 21st Century". In June 2002, the Animage readers voted One Piece to be the 16th best new anime of the year 2001, and gave it another 16th place in 2004 in the category "Favorite Anime Series". In a 2005 web poll by Japanese television network TV Asahi One Piece was voted 6th "most popular animated TV series". Before the poll, Asahi TV broadcast another list based on a nation-wide survey in which One Piece placed 4th among teenagers. In 2006, it was elected 32nd of the Top 100 Japanese anime by TV Asahi and 21st by its viewers. In September of the same year the Newtype magazine placed it 5th. Funimation's first DVD release of the series "One Piece: Season 1 First Voyage" was nominated for the Fifth Annual TV DVD Awards.
In Indonesia, Global TV was reprimanded by the Indonesian Broadcasting Commission (KPI) for airing the TV anime. Nina Armando, member of the KPI and lecturer at the University of Indonesia, said the show should not be aired at times when children are likely to watch.
In a review of the second DVD release of 4Kids Entertainment's dub, Todd Douglass, Jr. of DVD talk called its adaptation a "shabby treatment" resulting in an "arguably less enjoyable rendition". Douglass said that the 4Kids original opening was "a crappy rap song" and that the removal of whole scenes leaves a "feeling that something is missing". He later went on to say that "Fans of the 'real' One Piece will want to skip picking [...] up [4Kids Entertainment's One Piece DVDs] until an uncut release is announced", and also stated that "kids may get into this version because it's what they have seen on TV." Margaret Veira of Active Anime praised the TV series' "great" animation, stating that "It gives life and stays true to the style and characters of the manga." and noting the fight scenes in particular as having "a lot of energy to them". Patrick King of Animefringe comments that the art style of One Piece is "very distinctive and fresh". In a review of the first Funimation DVD release for Mania Entertainment, Bryce Coulter comments that One Piece is "not your typical pirate adventure" and that mixed with "the right amount of random fun along with a shonen style storyline" it becomes "an appealing and fun romp". In a review of Funimation Entertainment's second DVD release for Mania Entertainment, Bryce Coulter comments that "You can tell that they are giving One Piece the attention that was neglected by 4Kids" and that "One Piece is a great tale of high-seas fun that will leave you wanting more!"