A crooked man walks a crooked mile and gathers a crooked household to match, right down to the crooked cat and mouse. The repeated word is the whole game, and children love supplying it.
From Mother Goose / Nursery Rhymes (traditional). See the whole collection.
There was a crooked man, and he went a crooked mile,
He found a crooked sixpence beside a crooked stile;
He bought a crooked cat, which caught a crooked mouse,
And they all lived together in a little crooked house.
Public domain. Text from The Real Mother Goose (Blanche Fisher Wright, 1916), via Project Gutenberg. View the source edition