I have exactly the same problem with most of the songs I sing to my children. I was half thinking of starting a similar thread, but now someone else has, here goes for starters...
Does anyone know all the words to The Ash Grove? Ok, its sentimental Victorian claptrap, but I do find the tune irresistable.
And do any of you French speakers know all the words of Un oiseau m'a dit Bon Voyage, mon ami...
Another frustrating favourite with lots of humming is Yellow Bird up high in Banana Treeeeeee... I know the first verse, but there are a few gaps in the last part.
Any offers???