Nancy Sinatra (YouTube Link) - The original video of the original recording from 1966.
Mrs Miller (MP3) - The first cover version, also from 1966. Offbeat in every sense of the word.
Gypsy Boots And The Nature Boys (MP3) - Recorded in 1968 by Robert "Gypsy Boots" Bootzin, pioneer of the health food movement and founder of Tiki-styled health food store Health Hut. Grab the whole album Unpredictable! as part of the 365 Days Project.
The Residents (MP3) - The first song on their first LP Meet The Residents from 1974.
Destroy All Monsters in 1976 (MP3) and in 1981 (MP3) - What happened between these two recordings? Ex-Stooges guitarist Ron Asheton joined the band and (in his own words) "basically fired everybody" and "turned it into an actual playing band instead of clowns and noise-people".
Crispin Glover (MP3) - From Crispin's first (and unfortunately only) album The Big Problem ≠ The Solution. The Solution = Let It Be, from 1989.