1935 – from Jumbo
My Romance (Richard Rodgers, Lorenz Hart) was introduced in the Broadway extravaganza Jumbo, in which it was sung by Donald Novis and Gloria Grafton. The musical opened on Broadway at the Hippodrome Theatre on November 16, 1935 and closed on April 18, 1936 after 233 performances. Directed by John Murray Anderson and George Abbott it starred Jimmy Durante and a number of circus specialty acts. Jumbo tells the story of a financially-strapped circus. At the end of each performance, Durante lay down on the stage and permitted a live elephant to place its foot upon his head.
The large 5,000 seat theatre was turned into a circus tent where the various specialty acts (including acrobats and animal acts) performed during the show. The music was played by Paul Whiteman and his orchestra.  – Wikipedia extract, adapted
Mel Tormé – A date is not given; but the video provider attaches the following information about the singer
Mel Tormé was…best known for his classic jazz vocals. He was also a jazz composer and arranger, a drummer, an actor in radio, film, and television, and the author of five books. He co-wrote the classic holiday song “The Christmas Song” (“Chestnuts Roasting On An Open Fire”) with Bob Wells. His 1949 composition “California Suite,” became Capitol Records first 12-inch LP album. His singing at New York’s Copacabana led a local disc jockey to give him the nickname “The Velvet Fog”. This selection is from his album Thats All.
Ben Webster – Recorded: Live at De Hertenkamp Laren, The Netherlands September 2, 1970 — Personnel: Ben Webster – Tenor Sax, Cees Slinger – Piano, Rob Langeris – Bass, John Engels – Drums
Bill Evans Trio – with Marc Johnson – bass, Joe LaBarbera – drums, Iowa – 1979
John McLaughlin and Chick Corea – date unknown
Carly Simon – The title song and first track of a Simon album released on 22 Feb 1990
live c. 1990 at an Arista Records event
Jacques Lautier Quartet – 1993
The provider, Jacques, says (followed by my translation)
Un très beau morceau de Rodgers et Hart que j’interprète avec mon Quartet composé de Petro Garces à la basse, Marc Andreis à la batterie, Marcel Volberg aux percussions et moi-même Jacques Lautier au piano. Cela a été enregistré lors d’un concert au Club Frédirique de Vallauris le 11 novembre 1993.
A very beautiful piece by Rodgers and Hart that I interpret with my Quartet composed of Petro Garces (bass), Marc Andreis (drums), Marcel Volberg (percussion) and myself Jacques Lautier (piano). It was recorded during a concert at the Club Frédirique de Vallauris, 11 November 1993.
David Matthews and Friends, a group of musicians from the Manhattan Jazz Orchestra. I can always count on this band for the finale.
Little Girl Blue (m. Richard Rodgers, w. Lorenz Hart) was introduced at the Hippodrome in the show Jumbo (1935) by Gloria Grafton.
In his book The Song Is Ended: Songwriters and American Music, 1900-1950, William G. Hyland says, “The songs [from Jumbo] eventually caught on, but not at first because Rose insisted they not be played outside the theater, lest audiences lose interest.” That perhaps explains why Margaret Whiting’s version of “Little Girl Blue” didn’t chart until 1947 and played for only one week, topping at #25. It was left to vocalist/pianist Nina Simone to refocus attention on the song which became a signature tune for her in 1958 when she released her debut album entitled Little Girl Blue.
Frank Sinatra – recorded 6 November 1953; arranged by Nelson Riddle (based upon an arrangement by George Siravo according to the Sinatra discography at blue-eyes.com)
Hank Jones – recorded at Rudy Van Gelder Studios, Hackensack, New Jersey 1955 — Hank Jones: piano, Kenny Clarke: drums, Wendell Marshall: bass
The provider mentions that he recorded it from a radio broadcast in 2005.
Henry (Hank) Mobley (July 7, 1930 – May 30, 1986) was an American hard bop and soul jazz tenor saxophonist and composer. Mobley was described by Leonard Feather as the “middleweight champion of the tenor saxophone”, a metaphor used to describe his tone that was neither as aggressive as John Coltrane nor as mellow as Stan Getz. This description suggested to some that Mobley was mediocre. In addition, as his style was laid-back, subtle and melodic, especially in contrast with players like Sonny Rollins and John Coltrane, it took connoisseurs until after his demise to fully appreciate his talent. The critic Stacia Proefrock claimed he is “one of the more underrated musicians of the bop era.”
Hank Mobley Sextet – Rudy Van Gelder Studio, Hackensack, NJ – 20 July 1956 — Personnel:
Hank Mobley – Tenor Sax, Barry Harris – Piano, Doug Watkins – Bass, Art Taylor – Drums * Donald Byrd & Jackie McLean sit out
Judy Garland – record 6 February 1957 with an orchestra conducted by Gordon Jenkins
From her debut album, Little Girl Blue, released in 1958 — She repeatedly interpolates Good King Wenceslas as counterpoint on the piano
Montreux – 1976
Janis Joplin – from her 1969 LP I Got Dem Ol’ Kozmic Blues Again Mama!