Here's a complete list of all the covers done by The Fall if you want to hear some more.
Louie Louie - Richard Berry & the Pharaohs
Brand New Cadillac - Vince Taylor
Black Night - Deep Purple
Mr Pharmacist - The Other Half
Ghost In My House - R Dean Taylor
Victoria - The Kinks
Jerusalem - William Blake
A Day In The Life - The Beatles
Pinball Machine - Lonnie Irving
Race With The Devil - Gene Vincent
Black Monk Theme Part I - The Monks (Orginal Title - I Hate You)
Black Monk Theme Part II - The Monks (Orginal Title - Oh How To Do Now)
Popcorn Double Feature - The Searchers
White Lightning - The Big Bopper
Just Waiting - Hank Williams
Kimble - Lee Scratch Perry
Legend Of Xanadu - Dave Dee, Dozy, Beaky, Mick & Tich
Lost In Music - Sister Sledge
I'm Going To Spain - Steve Bent
Strychnine - The Sonics
Why Are People Grudgeful - Joe Gibbs
Jingle Bell Rock - Bobby Helms
War - Henry Cow
Junkman - The Groundhogs
Shut Up - The Monks
The City Never Sleeps - Nancy Sinatra
I'm Not Satisfied - Frank Zappa & The Mothers Of Invention
Beatle Bones 'N' Smokin' Stones - Captain Beefheart & His Magic Band
Birthday - The Idle Race
Stay Away (Old White Train) - Johnny Paycheck
Last Chance To Turn Around - Gene Pitney
I'm A Mummy - Bob McFadden & Dor
Jungle Rock - Hank Mizell
I Come And Stand At Your Door - The Byrds
Jet Boy - New York Dolls
Kill Your Sons / Ketamine Sun - Lou Reed
F-Oldin Money - Tommy Blake
Bound - The Audio Arts
This Perfect Day - The Saints
I Wanna Be Your Dog - The Stooges (Clint Boon w/ M.E.S.)
Bourgeois Town - Leadbelly
Gotta See Jane - R Dean Taylor
Ibis Afro Man - Iggy Pop
Classical Gas - Mason Williams
Groovin With Mr Bloe - Mr Bloe
Houston - Dean Martin
Walk Like A Man - Frankie Valli & The Four Seasons
I Can Hear The Grass Grow - The Move
Higgle-Dy Piggle-Dy - The Monks
White Line Fever - Merle Haggard
Coming Down - United States Of America
Hungry Freaks, Daddy - Frank Zappa & The Mothers Of Invention
Strange Town - The Groundhogs
And since people keep posting great big lists of songs Led Zeppelin have plagiarized here's a list of songs plagiarized by The Fall
Frightened - Hey Joe & Stepping Stone, both by Jimi Hendrix
Psykick Dancehall - Call Any Vegetable by Frank Zappa
No Xmas for John Quays - Up In Her Room by The Seeds & Why Do Fools Fall In Love? by Frankie Lymon & The Teenagers
Muzorewi's Daughter - Radio Story by Alternative TV
Rowche Rumble - Shake Appeal by The Stooges
Fiery Jack - Ring Of Fire by Johnny Cash
New Puritan - Kandy Korn by Captain Beefheart
How I Wrote ‘Elastic Man’ - Pictures Of Matchstick Men by Status Quo
Gramme Friday - Brand New Cadillac by Vince Taylor & The Play-Boys (& covered by The Fall)
The N.W.R.A. - Space Is Deep by Hawkwind
Slates, Slags etc - Rema Rema by Rema Rema
Hassle Schmuck - The Hucklebuck by Paul Williams & his Hucklebuckers
Detective Instinct - Mercenaries by John Cale
Marquis Cha-Cha - She Creatures Of Hollywood Hills by The Stooges
Papal Visit - Blue Bag by Can
Oh! Brother - Little Baby by The Blue Rondos
Draygo's Guilt - Vicious by Lou Reed
Clear Off - Semi-Multicoloured Caucasian by Captain Beefheart
Elves - I Wanna Be Your Dog by The Stooges
Mark'll Sink Us - Love Is Only Sleeping by The Monkees
Hey Marc Riley - Hey Bo Diddley by Bo Diddley
Barmy - Valeri by The Monkees
Gut Of The Quantifier - Funky Town by Lipps Inc
I Am Damo Suzuki - Oh Yeah by Can
To Nkroachment: Yarbles - Every Day I Have To Cry by Steve Alaimo/Dusty Springfield
Lucifer Over Lancashire - Devil In The Woods by The Gun Club
US 80's-90's - Obsession by The Passions
Athlete Cured - Tonight I'm Gonna Rock You Tonight by Spinal Tap
Wrong Place, Right Time - Gloomy by Creedence Clearwater Revival
Cab It Up! - TV Eye by The Stooges
Squid Lord - Junk Man by The Groundhogs
Sing! Harpy - Little Doll by The Stooges
The War Against Intelligence - Son Of A Preacher Man by Dusty Springfield
The League Of Bald Headed Men - Misty Mountain Hop by Led Zeppelin
Ten Houses Of Eve - Evil Hoodoo by The Seeds
Shake Off (Peel session version)) - Transmaniacon by The Walking Seeds
(Jung Nev's) Antidotes - Kashmir by Led Zeppelin
Touch Sensitive - I'm Waiting For The Man by Velvet Underground