The song has become a standard, with many recordings having been made of it. Among artists who have recorded it are Ella Fitzgerald, Louis Armstrong, Billie Holiday, Sarah Vaughan, Bing Crosby, Doris Day, Lena Horne, Frank Sinatra, Louis Prima, Diana Krall, John Barrowman, Lionel Hampton, Oscar Peterson, Nellie McKay, Erin McKeown, Joan Morris, and The Pogues with Kirsty MacColl. Nat King Cole, recorded it as the title track of his 1957 album "Just One Of Those Things". Peggy Lee recorded it in a stylized arrangement to become a chart topping hit in the 50's. Maurice Chevalier included it in a Cole Porter medley on his farewell album, released on his 80th birthday.
An episode of Get Smart alluded to the song: Agent 86 (posing as a mentally ill military officer) tells the psychiatrist he's investigating that he had been working on a space vehicle of his own: "gossamer wings," but lamented that "it was just one of those things."