My favorite version of this, by Ed McCurdy:

There's a hole in my bucket, dear Liza, dear Liza.
There's a hole in my bucket, dear Liza, a hole

Well mend it, dear Henry, dear Henry, dear Henry, well mend it, dear Henry, dear Henry, mend it

With what shall I mend it, deat Liza . . . with what
Well, mend it with straw, dear Henry . . . with straw

But the straw will fall out. . .
Well mend it with butter...

But the butter will melt...
Then take it to the tinsmith...

But the tinsmith costs money...
Oh well, then, don't bother...
I'll mend it myself!