Arab On Radar. A noise rock band with guitarists who didn't actually play real musical notes, a drummer that didn't play a smooth continuous drum beat, and a vocalist who yelled copious obscenity like a tone-deaf 10-year-old. YMMV, but this troper thinks they set a standard for awesome noise rock.
On a related note, Mars did the same thing in the mid-1970s, the key difference being the tone: Arab On Radar are kind of hilarious; Mars are utterly terrifying.
The hit of gay-as-a-maypole singer Thomas Bickham.
The second song was originally titled, "Eric Clapton's Kid Committed Suicide Because He Sucks." Seth Putnam, the man behind Anal Cunt, felt this was going too far. Both played straight and subverted.
Oh, oh, me too! How about "I Became A Counselor So I Could Tell Rape Victims They Asked For It" and "You Converted to Judaism So A Guy Would Touch Your Dick" and and... actually, all of them.
And for all those titles, the lyrics themselves are worse. Many of those titles had to be toned down for legal reasons. Just click the link above and see.
At the same time, this band explicitly avoids this by NOT spelling out their name on the album covers, abbreviating it to AC.
Even their logo is meant to be offensive—it's an anus and vagina, respectively, which get around the abbreviation.
The Muse music video for Knights of Cydonia is simply indescribable. It starts with Kung-fu cowboys and works its way up.
Springtime For Hitler. I watched it in history class. At first everyone looked on in uncomfortable horror, but around the time the actors started dancing around in the shape of a swastika, every single one of us was laughing helplessly.
It's the in-movie "horrified reaction" shots which truly put it over the top: "yes, we know exactly how appalling this is, and we're doing it anyway!"
Tom Lehrer. On his debut album, he included a ditty singing the praises of the neighborhood dope peddler. This was in 1953.
Tom Lehrer himself says that probably his most controversial song is "The Vatican Rag" which, of course, pokes fun at the Roman Catholic Church (specifically at Vatican 2's allowing 'modern' music to be used during Mass.) Even if you don't come from a religious background, it is downright hilarious, even more so if you're a former Christian. The recording, which is a live one, has the audience breaking out in laughter every few seconds. They really did find it just that funny.
Tom's introduction for the song gets quite a few laughs, too, especially when he says that the song he's about to perform is "a modest example". When it comes to Tom Lehrer, there is no such thing, and his audience is clearly well aware of that fact.
National Brotherhood Week: "Oh, the Protestants hate the Catholics, and the Catholics hate the Protestants. And the Hindus hate the Muslims, and everybody hates the Jews."
From the same song: "National Brotherhood Week, National Brotherhood Week: Lena Horne and Sheriff Clark are dancing cheek-to-cheek. It's fun to eulogize the people you despise as long as you don't let 'em in your schools...."
On the face of it, the popular Bloodhound Gang song "The Bad Touch" is a tactless solicitation of sex. But it gets away with its plethora of overtly sexual imagery because it's so ridiculously over-the-top, it becomes entertaining.
Not to mention their song "Foxtrot Uniform Charlie Kilo", which is a song entirely composed of sexual innuendo. And yes, the title DOES spell 'Fuck' in NATO phoneic spelling.
The music video takes it even further, with such things as a car shaped like a banana becoming unpeeled as it goes through a tunnel.
Die Ärzte are possibly the most famous and successful band in Germany of all time. Since their first days in the early 80s almost every song and music video is a Refuge in Audacity, and two of their early albums have been banned from being displayed on store shelves and played on concerts. In the face of changes in public perception and a rare instance of Reasonable Authority Figures, the responsible agency recognized that they Crossed The Line Twice, and repealed the ban on one in 2004.
Knorkator, another Berlin band known for even more ridiculous lyrics, also gets very close to crossing the line in about half of their songs. Some consists almost entirely of swearing or a overly poetic musings about masturbation or feces. "Schwanzlich Willkommen" (dickish welcome) tells that expression Herzlich Willkommen (hearty welcome) doesn't make any sense since a penis is much more suited as an organ to express happy feelings and in fact you can replace the word heart with dick in all expressions.
Of note is this life performance in which the two vocalists dressed up in tall, stripped cardboard boxes for the last song. At the end of the song, the guitarist appears back on the stage and, well, see for yourself.
Amanda Palmer's OasisCrosses the Line Twice by itself, being a peppy song about rape and abortion, ("I've seen better days, but I don't care/Oasis got my letter in the mail!") but the music video brings in the true audacity to take refuge in.
The Ball of Kerrymuir. Jim Croce is a family musician really - except for this one song, which is quite possibly the raunchiest thing you've ever heard. And it is absolutely hilarious. DefinitelyNSFW.
G.U.D seem to rely on this for their songs about anything. For example the song "Killing Pandas for Fun and Profit"
Killing
Pandas
For fun and profit
Turn their
Scrotum
Into a wallet
And it fun
To pretend you're killing nuns
Because they're black and white
But don't believe in an afterlife
Lou Reed's legendary "Walk on the Wild Side": while his peers were filling their albums and b-sides with shocking tracks, Lou Reed was the only one with the balls to release a single touching on full-time crossdressing, prescription drug abuse, male prostitution, a transwoman buying favors with oral sex (in a verse sometimes cut even today), and (perhaps most shockingly to modern audiences) a racial slur in the chorus, all in what's almost a bored monotone. And the song made top 40.
That's nothing. Ever heard "I Wanna Be Black"?
Or "Sex With Your Parents (Motherfucker) Part II". The gist of which is basically that all republican politicians are the way they are because, well, "When they looked into their lover's eyes, they saw MOM!"
"Weird Al" Yankovic deserves a mention here, as not many male performers would have the gall to dress up as Madonna and re-enact her own video's moves, shot for shot. Also, he always asks permission to write the parody, so the original artist ends up being condescending with the weirdness!
One of his Christmas songs, "Christmas at Ground Zero" (actually a parody of Yogi Yorgesson's "I Yust Go Nuts at Christmas") now counts as a "Funny Aneurysm" Moment. (The song is actually about Communists rather than terrorists.)
Sublime did this alot. Wrong Way is about a 12-year-old prostitute, Date Rape is also a good example. Although it should be noted that Bradley Nowell was attempting to say that these things were wrong. Other songs used profanity, drug references, etc, etc just for fun.
Flight of the Conchords - "If You're Into It". Writing a song to a girl? Cute. Suggesting, in said song, that you should get naked? Weird. Going on to suggest a food sex threesome? Hilarious!
KISS - tame now, but over-the-top when they first appeared. Beyond their image◊ and theatrics (blood-spitting, 12-inch platform boots, fire-breathing, explosions...), KISS' songs included "Nothing to Lose" (about anal sex, on their first album - in 1974!), "Goin' Blind" (a 93-year-old man in love with a 16-year-old girl who's also in love with him), "Larger Than Life" (Gene Simmons bragging about the size of his... "love"), "Shock Me" ("We can come together..."), and "Rocket Ride" ("Come on - grab ahold of my rocket!"). Drummer Peter Criss compared a KISS show to "surviving World War III." And of course, they ended up inspiring other bands to go even further, like...
Australian comedy singer/songwriter Kevin 'Bloody' Wilson was about to tour in Canada when he was warned not to use the c-word on-stage. His response? You Can't Say Cunt In Canada.
Tim Minchin in general, but (NSFW - cartoon penis) The Pope Song has got to take the cake. "Storm" is up there, too, with an anecdote about dinner ultimately becoming a ten-minute rant against all things "spiritual."
When an actor needs to establish themselves as "serious", they'll usually play a role that includes lots of sex, drugs and profanity. Natalie Portman had already done that and now needed to show that she wasn't all serious all the time. To do this, she took the road less traveled and rapped a song so absolutely violent and rude that it was just hilarious. With The Lonely Island. http://www.youtube.com/watch?v=PQjw9QkzGPU
Tom Maxwell's song "Ham" has an in-universe example crossed with Rule of Funny. A very large woman comes up to a cash register in a grocery store. Then a ham falls out from under her dress. She turns around and yells, "Who threw that ham at me?"