My Granny used to sing this to us all the time. Not sure if differences are localized or what, but this was her version (she was born in mountains of NC in 1930 and moved to eastern NC during the Depression)...

Was an old woman, had a little pig (mm mm mm)
Was an old woman, had a little pig (mm mm mm)
Was an old woman, had a little pig,
Didn't cost much 'cause he wasn't very big (mm mm mm)

This little piggy did lots of harm (mm mm mm)
This little piggy did lots of harm (mm mm mm)
This little piggy did lots of harm,
Runnin' and a snortin' all over the farm (mm mm mm)

The little piggy died from the lack of breath (mm mm mm)
The little piggy died from the lack of breath (mm mm mm)
The little piggy died from the lack of breath,
Wasn't that an awful death? (mm mm mm)

The old woman sobbed and she sighed and she cried (mm mm mm)
The old woman sobbed and she sighed and she cried (mm mm mm)
The old woman sobbed and she sighed and she cried,
Then she laid right down and died (mm mm mm)

The old man died because of grief (mm mm mm)
The old man died because of grief (mm mm mm)
The old man died because of grief,
Wasn't that a great relief? (mm mm mm)

There they all lie up on the shelf (mm mm mm)
There they all lie up on the shelf (mm mm mm)
There they all lie up on the shelf,
You want any more, you'll sing it yourself (mm mm mm)

(I used to love that last line!)
:)
Anyone else hear anything similar?