Robert Hugh Willoughby (Bob) was an American classical flute player and flute teacher. He played both Baroque and modern flute. He has been described by Flute magazine as the "American grandmaster of the flute."

He served as assistant principal flute in the Cleveland Orchestra under George Szell, and First Flute in the Cincinnati Orchestra under Max Rudolf.

Bob taught for many years at Oberlin College, where he was the first Robert Wheeler Professor of Performance. He taught for ten years at the Peabody Institute, and up until his death at the Longy School of Music of Bard College. In 1996 he received a Lifetime Achievement Award from the National Flute Association.