I also recommend:

Fiddler On The Roof

Gigi

The King and I

Sweeney Todd(not the movie although its not too bad, there was this live recording in the '80s of Angela Lansbury and George Hern doing the show, it is very good. George Hern IS Sweeney Todd)

Willy Wonka and The Chocolate Factory(the orignal, not the horrible remake)

Camelot(not the movie version, its terrible. There is a live recording of Richard Harris has doing the show at the Winter Garden theater. Imho, Harris gives a tour de force on the stage in that performance, much much better than the film)

of course, with any of the Broadway Musicals, the movie isn't the true way of experiencing it. The only way to truly experience a Broadway musical would be to go back in time and see the original cast performing it live on stage. Unfortunately that is impossible.