In respect of 'Hush Little Baby', I recalled that I kept a copy of the following posting from one the newsgroups. Unfortunately, I did not record the name of the poster. I found it quite interesting and perhaps you will too. I hope the formatting comes out okay - I tinkered with it as much as I could:

Query:
I'm looking for the lyrics that has "Hush little baby, don't you cry/ 's gonna sing you a lullaby". I think the song has been known colloquially as 'the Mockingbird song', although I'm not sure. I'm looking for the lyrics that have: "Hush little baby, don't you cry/ 's gonna sing you a lullaby". I think the song has been known colloquially as 'the Mockingbird song', although I'm not sure.

Answer:
I just happen to be working on that very song:

The lyric is built around the ethnic folk song "Hush Little Baby" (aka "Mockingbird Song"):

Hush little baby don't say a word,
Papa's gonna buy you a mocking bird
If that mocking bird don't sing,
Papa's gonna buy you a diamond ring,
If that diamond ring is brass,
Papa's gonna buy you a looking glass.

If that looking glass gets broke,
Papa's gonna buy you a billy goat,
If that billy goat won't pull,
Papa's gonna buy you a cart and bull.
And if that cart and bull turn over,
Papa gonna buy you a dog named Rover.

If that dog named Rover won't bark,
Papa's gonna buy you a horse and cart,
If that horse and cart fall down,

You'll still be the sweetest little baby in town.
This song is the basis of a children's "Hambone" song. Here's part of the lyric of the Bell Sister's version, which charted in 1952:
Hambone, hambone<
Where you been?
Round the world and I'm goin' again
What you gonna do when you come back?
Take a little walk by the railroad track
Hambone

Hambone, hambone
Have you heard?
Papa's gonna buy me a mocking bird
And if that mocking bird don't sing
Papa's gonna buy me a diamond ring
And if that diamond ring don't shine
Papa's gonna take it to the five and dime
Hambone.

The tune is a little like a popular army drill chant (which have the same kind of couplet structure). "The Hambone" is accompanied by "bones" or by body slapping. "Hambone" songs were seen early in the minstrel tradition. I guess that "knick, knack, paddywack, give a dog a bone" is another. One children's game is to see who can play the song the fastest.
The Lomaxes collected "Hush Little Baby" in the forties. J.C. Burris, who worked with Sonny Terry, had a version which Pete Seeger seems to have popularised (indeed, a 1964 Nina Simone album credits the song to Pete Seeger).

The song was reworked by Bo Diddley for the "first" rock 'n' roll song, in which the famous Bo Diddley beat emerged:

Bo Diddley bought his babe a diamond ring,
I that diamond ring don't shine
He gonna take it to a private eye,
If that private eye can't see
He'd better not take the ring from me

Bo Diddley caught a nanny goat,
To make his pretty baby a Sunday coat
Bo Diddley caught a bear cat,
To make his pretty baby a Sunday hat

Mojo come to my house, ya black cat bone,
Take my baby away from home
Ugly ole mojo, where ya bin,
Up your house, and gone again
Bo Diddley, Bo Diddley have you heard?
My pretty baby says she was a bird

The tune in this case is folk blues, in the Leadbelly open chord tradition. Pentatonic and little syncopation.
"Bo Diddley" influenced many rock songs, but that's another topic...

Cheers, Stewie.