I always knew it as:

Every time I go to town
Folks start kickin' my dog around
Even though he is a hound
They gotta stop kickin' my dog around

I used to sing it to my old dog, who because she was a bit of a thief when it came to food had a few boots in the butt in her time. I always thought it was just a bit of childhood doggerel (no pun) and had no idea that it was so widespread. I have heard the tune on the fiddle but just assumed that the fiddler was playing that hound dog song.