More:

THE HOODOO GURUS:  Bittersweet, I Want You Back
SPLITSVILLE:  Why It Can't Be
SAM PHILLIPS:  I Don't Know How To Say Goodbye To You
THE KNICKERBOCKERS:  Lies, She Said Goodbye
DUSTY SPRINGFIELD:  I Just Don't Know What To Do With Myself
CLIFF RICHARD:  Blue Turns To Grey (Rolling Stones cover, also done by 
The Flamin' Groovies, but Cliff's version is poppier)
THE 13th FLOOR ELEVATORS:  You're Gonna Miss Me
THE LEFT BANKE:  Walk Away, Renee


And an open question for Auditeers Assembled:

Is "September Gurls" a breakup song?  I could make a case for either 
answer.