The final collaboration between composer Richard Rodgers and lyricist Oscar Hammerstein II who passed away nine months after the opening, The Sound of Music opened at the Lunt-Fontanne Theatre on November 16, 1959 and would eventually become the second longest running Broadway musical of the Fifties, closing on June 15, 1963. The original production earned 5 Tony Awards, for Best Actress (Mary Martin), Best Featured Actress (Patricia Neway), Best Musical Director, Best Scenic Design, and tired for Best Musical with Fiorello! A Broadway revival opened on March 12, 1998 at the Martin Beck Theatre, starring Rebecca Luker, and was nominated for the Tony for Best Revival of a Musical. This production closed on June 20, 1999.
The show has been seen around the world, and in countless amateur productions, as well as, of course, the 1965 film. You can find a little more on the developement of the show here.