On Tom Lehrer's That Was The Year That Was, before the "National Brotherhood Week" song:
Lehrer: I'm sure we all agree that we ought to love one another, and I know there are people in the world who do not love their fellow human beings and Ihatepeople like that!
His inflections do make it clear that he's lampshadeing the trope, though.
For that matter, the whole joke of the song is based around the idea that a country with all the racial problems of America would set aside a week for brotherhood and tolerance — as the song says, "Be grateful that it doesn't last all year!"
Or indeed, as he notes in the other part of the opening monologue: "This year, on the first day of the week Malcolm X was killed, which should give you an idea of how effective the whole thing is."
Let's give in and all do the brotherhood bit Just make sure we don't make a habit of it Take an Indian to dine this week Show him we don't drawn the line this week We know ev'ryone can't be As American as we (After all, we came over on the Mayflower!)
Dan le Sac vs. Scroobius Pip, "Thou Shalt Always Kill":
Thou shalt not make repetitive generic music. Thou shalt not make repetitive generic music. Thou shalt not make repetitive generic music. Thou shalt not make repetitive generic music.
Korn's "Y'All Want A Single" is a Take That against the music industry. The music video is filled with protesting captions ("One Corporation Owns The 5 Major Video Channels In The U.S./ Is That OK?"; "Hit Songs On TOP 40 Are Often REPEATED Over 100 Times A Week", )... two of which resemble the song itself("90% Of All Songs Get To "The Hook" Within 20 Seconds./ 98% Of All # 1 Singles Are Less Than 3 Minutes and 30 Seconds Long."- the song is 3:17, and hits the hook at 0:17...), and the following one makes an... appropriate comment ("Does This Seem Like A Formula To You?"). Whether it's serious or humorous, it's up to you.
Think you're really righteous? Think you're pure in heart? Well, I know I'm a million times as humble as thou art!
Another example from him is "Achy Breaky Song", which uses the same tune as the song it's complaining about.
As well, "Don't Download This Song" deserves mention. The song itself doesn't seem that hypocritical, aside from the massive irony coming from the insane amounts of Slippery Slope Fallacy. Where does the hypocritical humor come in? Weird Al made the song available for download on his Myspace page a few weeks before the release of the song.
Monty Python's song "Never Be Rude to an Arab" starts off advising the listener to be racially tolerant, but informs you which races you should be tolerant to using racially abusive slurs.
In the original version of Morning Musume's Joshi Kashimashi Monogatari Takahashi Ai denies the claim that she still has her strong Fukui accent. She does so in Fukui-ben.
In one verse of Ben Folds Five's "Uncle Walter", the title character gives "a 50 minute lecture" about the dangers of smoking marijuana with "tobacco juice rolling off his chin".
Gogol Bordello's "Illumination" features the line "Of course there is no us and them / but them they do not think the same..."
Jesus He Knows Me by Genesis is about an unscrupulous televangelist. The hypocrisy is even more obvious in the video.
I believe in the family with my ever loving wife beside me
but she don't know about my girlfriend or the man I met last night
Won't find me practising what I'm preaching, won't find me making no sacrifice
But I can get you a pocketful of miracles, if you promise to be good, try to be nice
God will take good care of you, just do as I say, don't do as I do
A meta example could be those artists who insist that the authorities crack down on piracy so nobody steals their songs about being a wild outlaw who has no time for the police and sticks it to the man.
In "The Return of Sathington Willoughby" by Primus, there's a line about how "Paranoia is a disease unto itself." This is immediately followed up with a warning that "The person standing next to you may not be who they appear to be, so take precaution."
Tool's "Hooker with a Penis":
I met a boy wearing Vans, 501s, and a
Dope Beastie T, nipple rings, new tattoos
That claimed that he was OGT,
back from '92, the first EP.
And in between sips of Coke he told me
That he thought we were selling out
Laying down, sucking up to the man.
Knorkator's "Kinderlied" (children song) is about the exploitation of the children of celebrities. It's sung by the song writers young son. Played for laughs by making their fathers sound like washed up musicians who have lost all their dignity and not yet realized that nobody cares for them anymore.
The Green Bay Packers fan-song "Da Bears Still Suck" makes fun of the Chicago Bears for (among other things), having only won a single Super Bowl, This despite the fact that at the time the song was recorded, the Packers themselves had only a single Vince Lombardi trophy.
The band Ookla the Mok, who do pretty much nothing but songs about comic books, did a song called "Stop Talking About Comic Books or I'll Kill You". For bonus points, the last line of the song is the singer asking his comics-obsessed friend to pick up the latest The Invisibles for him.