[Michael.SF.]

LOL

Since you mentioned Rufus Thomas:

Walking the dog

[BluesDuke]

Since you mentioned Rufus Thomas:

Rufus Thomas, "The Dog"
Rufus Thomas, "Can Your Monkey Do the Dog"
Rufus Thomas, "Do the Funky Chicken"

Meanwhile . . .

Talking Heads, "Animals"
Stick McGhee, "One Monkey Don't Stop No Show"
Major Lance, "The Monkey Time"
The Graham Bond Organisation, "Camels and Elephants"
Blind Lemon Jefferson, "Rabbit Foot Blues"
Jefferson Airplane, "White Rabbit"
La Vern Baker, "Gimme a Pigfoot"
The Beach Boys, "Mrs. O'Leary's Cow"
Willie Dixon with the Big Three Trio, "I Ain't Gonna Be Your Monkey Man No More"