In the song "Necessity" from Finians Rainbow, the lines quoted below provoke the shouted question "Do you mean he's a —?", which is answered in the affirmative (the implied statement being that Necessity is a bastard):
Oh, hell is the father of gin, And Cupid's the father of love. Old Satan's the father of sin, But no one knows the father of Necessity.
It also seems to be a stealth pun on the saying "Necessity is the mother of invention."
"Girl Anachronism" by The Dresden Dolls: about a girl who blames her constant sickness on having been born too soon by C-section. Including the line "You can tell (...) that I'm not right now at all."
During his polka medley "Polka Face", "Weird Al" Yankovic breaks into an accordion solo immediately after the "Break Your Heart" section. The obscure song is actually an instrumental version of the "Tick Tock Polka" originally done by polka-meister Frankie Yankovic (no relation). Appropriately enough, this leads directly into his version of Kesha's "TiK ToK".
At one point in "Handy", the repairman narrator refers to his "bag of tricks", a Felix the Cat reference that is reaffirmed by the video. It is not mentioned that this would make him Fix-It Felix.
The cover of R.E.M.'sLifes Rich Pageant is a Visual Pun: It's a collage depicting band member Bill Berry and a pair of bison... as in "Buffalo Bill".
The textless cover of The Pixies' "Gigantic" single is a photograph of a crying naked baby, while the back cover has a picture of a driving glove laying on the ground. This may seem like a True Art Is Incomprehensible sort of thing, until you realize it's actually a play on a potential mondegreen of the song: "A baby glove" instead of "A big, big love".
The real name of 2D, lead singer of Gorillaz, is Stuart Pot, a.k.a. Stu-Pot. He spent some time in a coma. At least one fanfic, but nobody in the canon, has pointed out that this would make him a vegetable Stu.
"Flowers On The Wall" by The Statler Brothers: "Playin' solitaire 'til dawn with a deck of fifty-one." The narrator's missing one card... he's not playing with a full deck.
Speaking of guns, puns and the Fab Four, there's their album Revolver, which would originally have been played on a turntable, thereby "revolving".
The Divine Comedy song, "The Complete Banker", which is about the role of the banks in the current recession. From his point of view, he's a complete banker, but we'd rather call him a complete wanker.
The main chord sequence for AC/DC's "High Voltage" is A, C, D, C.
There's a Linkin Park song called "Cure for the Itch," which is instrumental and performed solely by Joe Hahn, who plays turntables. He's scratching.
Mac McAnally's "Back Where I Come From":
We learned in the Sunday school
Who made the sun shine through
I know who made the moonshine, too
Back where I come from
"Rollin' (The Ballad of Big & Rich)" by Big & Rich has two. The first is "Charley Pride was the man in black / Rock & roll used to be 'bout Johnny Cash", and the other is "I'm a crazy son of a [bad word] / But I know I'm gonna make it big and rich".
The Rush song "Roll the Bones" deals with questions of existence and causation in a funkier style than the band's usual prog-rock fare. In other words, it's existential funk.
Dallas Green didn't want to put just his name on the cover of his first acoustic solo album, so what did he name his act? City & Colour.
There's a possible unspoken Visual Pun in Boards of Canada's "Dayvan Cowboy" video - at one point it has footage of Laird Hamilton surfing, which makes sense when you think of other meanings of the word "boards".
In Jonathan Coulton's acoustic cover of Sir Mix-a-Lot's "Baby Got Back," the "quack" sound effect makes a lot more sense when you think of the line in which it appears like this: "But I gotta be straight when I say I wanna [duck] till the break of dawn."
Bo Burnham does this on a regular basis. There are too many instances to count.
Once Executive Meddling forced Beatallica to record Abbey Load with the original lyrics by The Beatles instead of their comedic Beatles meetMetallica ones, aside from one who kept the parody chorus ("For Whom Michelle Tolls!"), the rest force listeners to pay attention to the musical backdrop and understand why said Metallica song is there. For instance, "Come Together" is "Through the Never" ("Come Through the Never"), the acoustic instrumental cover of "Blackbird" resembles the opening for "Fade to Black" ("Fade to Blackbird"), others are right in the title ("Sun King" = "King Nothing", "She Came In Through the Bathroom Window" = "Dirty Window", "The End" = "The End of the Line") and one is as stealthy as possible ("Golden Slumbers" = "Until It Sleeps").