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Kyu Sakamoto - Sukiyaki
(look for the Zona Visser English version, which is the best English version)
Edith Piaf - A quoi ca sert l'amour
(everyone knows her for Je Ne Regrette Rien, a dirge beloved of advertisers, but she was incredibly talented beyond that and produced a whole range of songs)
Also, before it became a meme in the form of the Numa Numa Song, Dragosta Din Tei by O-Town was very catchy and even made it onto the charts.