No doubt the members of The Who were familiar with the original version by Johnny Kidd and the Pirates who released the song in 1960. Kidd’s version was only released in the UK where it was a #1 record.
Johnny Kidd & the Pirates version – ignore the Elvis video
As with most North Americans, I am familiar with the version done by The Guess Who. It is my understanding that the original release of this single was issued in Canada under the band’s former name, Chad Allen and the Expressions. The name Guess Who came about because Scepter Records (their U.S. label) feared that a Canadian band during 1965’s “British Invasion” might be ignored by American radio.
Scepter decided to issue white label promo copies with no band name except, “Guess Who?” The purpose was to generate interest and it worked. Since the name stuck, Chad Allen and the Expressions became “The Guess Who” and subsequent issues of the record in Canada as well as the American album on Scepter were issued as “Chad Allen and the Expressions (Guess Who?).” By the way, "Shakin' All Over" charted at 22 in the U.S.
Being that this is the first version which I have been exposed, it is my favorite. The piano, which is absent from the original version by Kidd, is the glue that makes The Guess Who's rendition superior. With that said, Kidd’s original is pretty good as well. I listened to several covers of this song and most carry through the whammy bar guitar parts that carried through from Kidd's version and became a signature sound of this tune.