I realize that Noreen's request has been well and completely answered, but the first song I thought about is one that begins,

Close your eyes, Lena, my darling while
   I sing your lullabye- O lullabye my Lena, my darling
( la la la la...don't remember words to this line)

Chorus was something like:
Go to sleep my ba-a-by, my ba-a-by, my ba-aaa-by;
Go to sleep my ba-a-by, my ba-a-by, my ba-byyyyy.

My older sisters sang it, and they told me it was from a Broadway show. Anyone know what show it was? It's a lovely tune, and is usually half sung, half hummed- the way lullabyes often are. The very last note is sung or hummed an octave higher than the note before it- ba-byyyy... Thread creep, I know, Noreen, but I couldn't resist asking the experts if they know this one! Jean