It's pretty likely that I'm never going to stop adding to this list:

THE SMITHEREENS:  Cigarette
THE KINKS:  Days, No More Looking Back
THE HOLLIES:  So Lonely (also covered by....)
THE EVERLY BROTHERS:  Bye Bye Love, Gone Gone Gone, Since You Broke My 
Heart, The Girl Who Sang The Blues, many more
THE FLASHCUBES:  Gone Too Far, She's Leaving
THE BEAU BRUMMELS:  You Tell Me Why, Just A Little
STIV BATORS:  It's Cold Outside (covering....)
THE CHOIR:  When You Were With Me, I'd Rather You Leave Me
THE LYRES:  But If You're Happy
MANNIX:  Highway Lines