Banned by the BBC - even though the BBC always denied that they have ever banned a song from radio, here is the list of songs beleived to have been banned.

Sexual Nature

• Jane Birkin - Je T?aime - Maybe it wasn't helped by Serge Gainsbourg singing about the joys of going "entre tes reins" - between your kidneys - i.e. up your bum (alledgedly). On top of the pops an instrumental version by "Sounds Nice" was used - 1969 & 1974
• Frankie goes to Hollywood - Relax - Sexual references - 1983
• The Au Pairs - Come Again - Referred to orgasm - 1981
• Lil Louis - French Kiss - "Heavy breathing" - 1989
• The New Yorkers - Love For Sale - "Sexual" content - 1930??
• Judge Dread - Several records with titles as Big 6, Big 7,Big 8, 10 etc - "Sexual" content - 1972 - 1975
• Ivor Biggun - The winker's song (misprint) - Sexually explicit - 1978
• Troggs - I Can?t Control Myself - The sound Reg Presley makes at the end of the song  was said to be like someone climaxing. - 1966
• Rolling Stones - Lets spend the night together - Promoted promiscuity - 1967
• Cliff Richard - Honky tonk angel - Self imposed ban as "saint" Cliff didn?t know that a Honky tonk angel was a Hooker! circa ?72 -?73.
• Adam Faith - Made You - Banned for lewdness/Sexual Content Double A-Side with "When Johnny Comes Marching Home" - 1960
• The Stranglers - Peaches - Considered "woman baiting" - 1977
• Scott Walker - Jackie - Reference to "authentic queers" - 1967
• George Michael - I Want Your Sex - banned only before the "watershed" - 1987
• Paul McCarney & Wings - Hi Hi Hi - Banned, not due to drug references but to explicit sexual lyrics - 1972
• Joe Brown & The Bruvvers' revival of George Formby's "My Little Ukelele" (1963, Piccadilly/Pye) was banned as "too risque"
• Max Romeo - Wet Dream - A song about his bedroom ceiling. No the BBC wouldn't buy that - 1969
• Donna Summer - Love to love you - Groans & heavy breathing secured the ban - 1976
• The Prodigy - Smack my bitch up - Despite denials, this single was never herd during the day - 1997
• Pete Shelley - Homosapien  -  "SPIN Alternative Record Guide." The book claims "Homosapien" was banned for containing the line "Homo superior in my interior."(About 1982)
• Yoko Ono Plastic Ono Band - Open Your Box -  From the album of the same name and B side of a single, it was banned for containing the lyric "open your legs" - 1970

Political Nature

• Marxman - Sad Affair - Contained IRA slogan - 1993
• Police - Invisible Sun was banned (certainly by R1/TOTP, maybe others)
  references to Northern Ireland (Barrel of an Armalite, etc.) - 1981
• Paul McCartney - Give Ireland Back to the Irish - Obvious - 1972
• Johnny Horton - Battle of New Orleans - Reference to "Bloody British" - 1959
• Hawkwind - "Urban Guerrila" - early 1970's. Banned due to mainland UK terrorist attacks at the time.
• Sex Pistols - God Save the Queen - Anti monarchy - 1977
• Blow Monkeys - The Day After You - Anti Margaret Thatcher - 1987
• Split Enz - Six Months In A Leaky Boat - Too provocative (Falklands) - 1980
• Elaine Page/Julie Covington "Don't Cry for Me, Argentina" Falklands Crisis - 1980
• McGuiness Flint - Let the people go - Government policy on the IRA - 1975
• Heaven 17 - (We Don't Need This) Fascist Groove Thang" - The "All-Music Guide"  says  "Fascist Groove Thang" was banned by the BBC for its overtly political nature. (About 1981)
• Six Months In A Leaky Boat. - 'Split Enz' 1984 - During the Falklands war, their song that went 'I just spent six months
  in a leaky boat, Lucky just to keep afloat.'

Political 2 - The Gulf War 1

All these recordings were banned during the gulf war in 1990. 

• Jose Felicano & The Doors - Light My Fire
• Something Happens - "Parachute"
• The Cure - Killing an Arab
• Little angels - Bone yard
• Massive Attack had the word "attack"  dropped during the gulf war.
• Bomb the Bass also suffered during this period.

?The Word,? listed 64 songs on its February 1st program that BBC Radio have deemed "unsuitable" to play during the Gulf Crisis:  

• Abba Waterloo
• A-ha Hunting High And Low
• Alarm 68 Guns
• Animals We Got To Get Out Of This Place 5.
• Arrival I Will Survive 6.
• Joan Baez The Night They Drove Old Dixie Down 7.
• Bangles Walk Like An Egyptian 8.
• The Beatles Back In The USSR 9.
• Pat Benetar Love Is A Battlefield
• Big Country Fields Of Fire
• Blondie Atomic
• Boomtown Rats Don't Like Mondays
• Brook Bros. Warpaint
• Arthur Brown Fire
• Kate Bush Army Dreamers
• Cher Bang Bang (My Baby Shot Me Down)
• Eric Clapton I Shot The Sheriff
• Phil Collins In The Air Tonight
• Cutting Crew I Just Died In Your Arms Tonight
• Skeeter Davies End Of The World
• Desmond Dekker Israelites
• Dire Straits Brothers In Arms
• Duran Duran View To A Kill
• Jose Feliciano Light My Fire
• First Choice Armed And Extremely Dangerous
• Roberta Flack Killing Me Softly
• Frankie Goes To Hollywood Two Tribes
• Eddie Grant Living On The Frontline
• Eddie Grant Give Me Hope Joanna
• Elton John Saturday Night's Alright For Fighting
• Johnny Hates Jazz I Don't Want To Be A Hero
• John Lennon Give Peace A Chance
• John Lennon Imagine
• Jona Louis Stop The Cavalry
• Lulu Boom Bang A Bang
• McGuinness Flint When I'm Dead And Gone
• Bob Marley Buffalo Soldier
• Maria Muldaur Midnight At The Oasis
• M*A*S*H Suicide Is Painless
• Mike And The Mechanics Silent Running
• Rick Nelson Fools Rush In
• Nicole A Little Peace
• Billy Ocean When The Going Gets Tough
• Donny Osmond Soldier Of Love
• Paper Lace Billy Don't Be A Hero
• Queen Killer Queen
• Queen Flash
• Martha Reeves Forget Me Not
•  B.A. Robertson Bang Bang
•  Tom Robinson War Baby
•  Kenny Rogers Ruby (Don't Take Your Love To Town)
•  Spandau Ballet I'll Fly For You
•  Specials Ghost Town
•  Bruce Springsteen I'm On Fire
•  Edwin Starr War
•  Status Quo In The Army Now
•  Status Quo Burning Bridges
•  Cat Stevens I'm Gonna Get Me A Gun
•  Rod Stewart Sailing
•  Donna Summer State Of Independence
•  Tears For Fears Everybody Wants To Rule The World
•  Temptations Ball Of Confusion
•  10 CC Rubber Bullets
•  Stevie Wonder Heaven Help Us All

Morbid Nature

• The Moontrekkers - Night Of The Vampire - morbid /"scary" content (backing group to Rod Stewart, produced by Joe Meek - 1961
• Sam M.Lewis - Gloomy Sunday - Too mournful - 1930??
• Mike Berry & The Outlaws - Tribute To Buddy Holly -"morbid concern" for a dead teenage idol - A Joe Meek masterpiece - 1961
• Ricky Valance - Tell Laura I love her - banned because of the reference to dying in a stock car race? - 1960
• The Downliners Sect's 1965 EP, "THE SECT SING SICK SONGS" was banned for poor taste/morbidity; it included a cover of Jimmy Cross' - I WANT MY BABY BACK (where a necrophiliac boyfriend digs up & jumps in his girlfriend's coffin)
• Napoleon XIV - They're coming to take me away ha-haaaa - Preceded rap by some 25 years. Man going bonkers over lost dog - 1966
  

Advertising

• Paul Simon - Kodachrome - Advertising - 197?
• The Kinks - Lola - was originally banned because it mentioned Coca-Cola, was later changed to Cherry Cola to get airplay. - 1970
• Paul Simon - Me and Julio - Originally banned for referring to Newsweek magazine. - 1972
• Dr Hook & the Medicine show - The cover of Rolling Stone - Advertising - 1972
• Dr Hook & the Medicine show - The Cover of the Radio Times - Tried to get around the ban by sucking up to the BBC with this version! - 1972
• Danny Williams - "You're Fabulous Babe" - 1977. Banned due to advertising. Babe was a perfume.
• Pink Floyd  - IT WOULD BE SO NICE,  April  1968. The lyrics mentioned the British newspaper The Evening Standard. The record could not be played on UK radio. As a result,  Pink Floyd had to spend about $1000 to replace the Evening Standard with Daily Standard to appease the BBC. The record failed in the charts despite the touch of controversy. Another thing, the copies sold in shops were the Evening Standard version,  but all releases available now are the corrected version. 
• Jimmy Buffett's single, "come Monday" contained the line, "I've got my Hush Puppies on." Since the BBC considered this to be advertising he re-recorded that line so it said, "I've got my hiking shoes on." 

F Word - Part 1

In resent years this category would be overflowing - here are a few key offenders.

• Super furry animals - The man don't give a f_ck - 50 odd uses of the F word - 1996
• John Lennon - Working Class Hero - 1970
• Ian Dury - "F-cking Ada" - 1980 - Use of F word?
• Black Grape - "Shake your money" - 1995 Use of F word.
• The Dead Kennedys - Too Drunk To F-ck - Can't think why this should receive a ban?
• Neil Young - F-cking up - 1990
• Fatboy Slim  - F-cking in heaven - 108 uses of the F word! - 1998
• Linda McCarytney - The light comes from within - Even the inclusion of the F word & being dead  she can't get a hit! - 1999
• Richie Kavanagh  - "Aon Focal Eile"   Banned in Britain because first  syllable of  "Focal", (the Irish for "Word") sounded too much like "F-ck"...
• The Rolling Stones - Star Star.  Despite the title being changed, the words star f-cker (repeated dozens of times) could still be herd in the chorus! - 1973 

Banned but saved by the radio edit - F word part 2

• Radiohead - Creep - Edited to make the F word disappear - 1992
• Beautiful South - Don't marry her have me - Originally titled and contained the line "Don't marry her f-ck me" - 1996
• Prince's "Sexy Motherf-cker" which was renamed "Sexy MF" 1992
• The Stranglers - "Peaches" The lyrics were changed for radio. 1977
• XTC - "Respectable Street", from '82, lyrics about abortion, sex positions, and neighbors retching over each other's fences were replaced.
• Monty Python's "Always look on the bright side of life" where "Life's a piece of shit / when you think of it" was replaced to suit the BBC's tastes. 

Miscellaneous

• Nero & The Gladiators' - "Hall Of The Mountain King" was banned for its spoken intro-a short beatnik query about the location of "the king's pad" - 1961
• Roberta Flack - Killing me softly - Reason Unknown - 1973
• Mungo Jerry - Have a Whiff on Me - Drug references - 1971

Banned by "Top of the Pops" (BBC)

• D-Mob - We Call It Acieed - Drug reference - 1988
• The Pogues - A pair of brown eyes - Video ban - 1985
• Bjork - Alarm Call - For her animated nipples! - 1998
• Lonnie Donegan - Digging my Potatoes -   1956

Banned in the USA (Possibly in the UK too)

• The Beatles - A day in the life - Banned in the '60's for drug references - 1967
• Rolling Stones - Stoned - Original B side to I Wanna be your man - Drug references - 1964
• Ten Years After - Good morning Little Schoolgirl - Under age sexual references - 1969
• Chumbawamba - We Are the World - Explicit direct action support - 1985
• Junior Delgardo - Broadwater Farm - Prophecising riots - 1985
• Mark Dinning - Teen Angel - Called a "death disk" - 1960
• Falco - Psycho Terror - Line "all Vienna is on heroine" - 1979
• The Heptones - Fattie Fattie - Lewd and suggestive
• Napolean XII - There Coming to Take me Away - Reference "mentally challenged" - 1966
• Smoke - My Friend Jack - Was indeed banned because of drugs refs (my friend Jack eats sugar lumps, my friend Jack eats sugar lumps ... he's been travelling everywhere) - 1967
• Eurythmics - Sex Crime (1994) - Reapeated use of the words 'Sex' & 'Crime' - 1984
• Chef - Chocolate salty balls - 1998 -Apparently the US public have filthy minds!

Other Mentions

• Although the Marvin Gaye Record Sexual Healing was not banned, The DJ?s On UK's national "Radio One" had to drop the word "sexual" from the title!

• Tom Petty's "You Don't Know How It Feels" was censored on MTV so that the line "let's roll another joint" became "lets hit another joint."
  When the video is shown on VH1, "roll" is left in, but the word "joint" is mangled so that it is impossible to make out (it sounds like the word is being played backwards).

• Brian Eno's Album "My life in the bush of ghosts" now exclude the track "Qu'ran" (in the UK) due to serious fatwahs from Islamic fundamentalists.