One piece of music that always makes me go weak at the knees: the quartet "Mir ist so wunderbar" from Beethoven's "Fidelio". The camerawork is slightly static, the singing is anything but.
PS: Sorry - I'd forgotten that the names of the performers only appear when you go directly to YouTube itself. They are Lucia Popp, Gundula Janowitz, Manfred Jungwirth and Adolf Dallapozza. Leonard Bernstein conducts the Vienna Philharmonic.