"Rhapsody in Blue" (George Gershwin)

George Gershwin had earned renown writing jazz-inflected pop tunes and music for Broadway in the late 1910s and early 20s.  But no one (perhaps even Gershwin himself) anticipated that he would win acclaim as a classical music composer.
It was late 1923, and famed bandleader Paul Whiteman was making plans to stage a concert in February 1924 at New York's Aeolian Hall to, once and for all, legitimize jazz as an accepted art form.  The gist of the "Experiment in Modern Music" performance was to show how jazz and classical idioms could intertwine through a series of educational/experimental performances.
The year before, as part of the Broadway musical revue Scandals of 1922, Whiteman had conducted the orchestra for Gershwin's Blue Monday, a one-act jazz opera that transported Leoncavallo's Pagliacci from Calabria to a basement bar on Harlem's 135th Street.  It flopped.  In fact, it went over so poorly with the audience and critics that it was removed from all subsequent performances of the revue.  Nevertheless, the ambitious piece made such an impression on Whiteman that Gershwin was his logical first choice when commissioning an original work for the upcoming Aeolian Hall concert.
But Gershwin turned him down flat.  He told Whiteman that there was no way he could write and refine a brand new composition (without embarrassing them both) in the few weeks between the New Year and the February show.
Gershwin didn't give Whiteman's commission another thought until his lyricist brother, Ira, showed him an article in the New York Times, which quoted Whiteman as saying that George was hard at work on an experimental piece of music for the Aeolian Hall show.
Being over a barrel, Gershwin set about writing the composition with only 5 weeks to spare and work left to do on a brand new musical, Sweet Little Devil, which was set to open on January 21.
While on the train to Boston in mid-January to "test market" Sweet Little Devil before its formal debut on Broadway, the first pieces of what Gershwin was tentatively calling his American Rhapsody started to fall into place.
"I suddenly heard—and even saw on paper—the complete construction of the rhapsody, from beginning to end…I heard it as a sort of musical kaleidoscope of America—of our vast melting pot, of our unduplicated national pep, of our blues, our metropolitan madness."
The final piece of the puzzle came at a cocktail party back in New York, where the composer was noodling around on piano, as he often did.  Ira was nearby listening and realized that the improvised theme George was playing—that grand, andante section that United Airlines has famously used in its commercials since 1987—should be the finale of the piece.
The final title of the work was suggested by Ira, too.  Having visited an exhibition of James Whistler's paintings, Ira was inspired by the titles of several of the works (Symphony in White, No. 1; Nocturne: Blue and Gold; Arrangement in Gray and Black—a.k.a Whistler's Mother).  Ultimately, it was decided by the brothers Gershwin that the piece should be called Rhapsody in Blue.
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I love this piece of music in any form.  And while I'm very fond of the fully orchestrated version with its signature glissando clarinet wail at the start, there's another version that is my personal favorite, which is embedded below.
Back in 1993, pianist and music historian Artis Wodehouse compiled the album Gershwin Plays Gershwin: The Piano Rolls, using Yamaha's Disklavier technology to read and interpret player piano rolls that Gershwin had cut for the Duo-Art Piano Roll company in the 1920s.  In essence, what you hear on the recording is Rhapsody in Blue in its purest, simplest form: Gershwin himself on piano, circa 1927, playing his heart out.
Gives me chills every time I listen to it.