In Lupe Fiasco's character biographies for The Cool, Michael Young History's birthdate is listed as the day Lupe's first album Food and Liquour was leaked. The Cool's is listed as six months later, a reference to the line in the song The Cool. Yes, there's a song, a CD, and a character all named The Cool.
In Voltaire's song Alchemy Mondays, in the middle he stops to say "Hold everything they're playing my song!" and he sings part of one of his most famous songs, When You're Evil, and then continues with the song.
The Beatles song "Glass Onion" is one long series of references to their earlier songs in the same surreal mode, mostly mainly-Lennon works: "Strawberry Fields Forever", "I Am The Walrus", "Lady Madonna" and "The Fool on the Hill".
"Lady Madonna" is mainly-McCartney, "Fool on the Hill" entirely so: Paul is the only Beatle to play on the latter track.
And "I Am The Walrus", in itself, name-checks a song from the previous album: "See how they fly, like Lucy in the sky, see how they run..."
"Glass Onion" also references the infamous "Paul is dead" rumors that some conspiracy buffs floated at the time with the line, "And here's another clue for you all,/The Walrus was Paul". Post-Beatles, John Lennon wrote a line for the song God: "I was the Walrus, but now I'm John."
The Rolling Stones' "Flight 505" opens with a boogie-woogie piano intro that segues into in the famous "Satisfaction" riff before launching into the song proper.
Hey, Mr. DJ, I Thought You Said We Had a Deal name-checks The World's Address, Rabid Child, and Chess Piece Face.
I'm Sick (of This American Life) cribs lyrics from Cyclops Rock and I've Learned the Value of Human Sacrifice.
How Can I Sing Like a Girl? was inspired by John Flansburgh having to sing in falsetto during live performances of She Was a Hotel Detective.
And that song has been interpreted as an allegory for the band's transformation around that time.
Managing to pull this off on their first album, Rhythm Section Want Ad details various things the band dealt with after their demo tape earned them attention from the NYC music scene — the song title is a specific complaint one exec had about the (then-)drum machine-reliant band.
The song Sweet and Low by Strippers Union has the line, "It's not his suits that got the girl." This is a reference to the Odds song Someone Who's Cool, with its lyric: "It was the suit that got me the gig, it was the tear that got me the girl." The gag being that Craig Northey, Doug Elliott and Pat Steward are members of both bands.
Veruca Salt's song "Volcano Girls" references their past hit song "The Seether", with the line "Well, here's another clue if you please/The Seether's Louise" (as in Louise Post, one of the band's former leaders). This is also a reference to the aforementioned Beatles song "Glass Onion".
Tommy and Gina, from Bon Jovi's "Living On A Prayer", are referenced fourteen years later in "It's My Life":
And this is for the ones who stood their ground For Tommy and Gina, who never backed down.
Tommy and Gina didn't have to wait 14 years for a name check. They're mentioned in "99 in the Shade" off of the New Jersey album.
Somebody tells me even Tommy's coming down tonight If Gina says it's all right.
Steve Miller name checks three of his previous songs in the opening lines of "The Joker" ("Space Cowboy," "Gangsters of Love" and "Enter Maurice"). Of course The Joker became a much bigger hit than any of those, to the point mentioning the earlier songs often confuses people. (When Rock Band released both Space Cowboy and The Joker simultaneously, many were confused, thinking they were the same song.)
Bad Religion's "21st Century Digital Boy" references two of their past songs near the end, "Suffer" and "No Control."
Hip Hop artist notoriously reference past songs, possibly the best example being Dr. Dre and Snoop Dogg's "The Next Episode," a reference to a throwaway line from the song "Nuthin But a G Thang."
In Men Without Hats' song "Pop Goes The World", the lines "And every time I wonder if the world is right,/End up in some disco dancing all night" are followed by about three bars of a distinctive melody from their earlier hit, "Safety Dance".
Gary Cherone of Extreme (and formerly of Van Halen and Tribes of Judah) has been known to reference lyrics from bands he's been influenced by. When Extreme reunited in 2008 with their album "Saudades de Rock" the song "Sunrise" featured the lyrics "She don't need to beg or borrow", a reference to "Runnin' With The Devil", by the David Lee Roth era Van Halen.
While he was briefly sitting in as Van Halen's third frontman, the song "Dirty Water Dog" featured the phrase "under the sun", which is a throwback to an Extreme triptych (3-part song) entitled "3 Sides To Every Story". The second part of which was entitled "Everything Under The Sun".
Additionally, the Van Halen tune "How Many Say I", also written by Cherone, features the phrase "all you need is love". A Beatles reference if ever there was one.
The song "God Isn't Dead?", again, by Extreme, begins with the words, "Aahh, look at all the lonely people". This one's an obvious shout-out to The Beatles "Eleanor Rigby".
The break at the end of the guitar solo in "Rest In Peace" features a musical quote from Jimi Hendrix's "Voodoo Chile (Slight Return)".
Eminem does this multiple times, particularly when he name checks Dr Dre. "My Name Is..." sets up the joke:
Eminem: And Dr. Dre said... Dre: Slim Shady is a basehead?! Eminem: Uh-uh! Dre: Then why's your face red? Man, you wasted!
Cue "The Real Slim Shady":
Eminem: And Dr. Dre said... nothing, you idiots, Dr. Dre's dead! He's locked in my basement!
Ian Anderson references life as being a "passion play" in various songs. A Passion Play was one of Tull's most successful albums.
The Passion Play album refers to "life's long song". A 1971 single of theirs is "Life Is A Long Song".
The song "Mountain Men" on Crest Of A Knave has the line "And who am I to fast deny the right to take a fish once in a while", alluding to his real life salmon farming pursuits.
In "Strange Avenues", he mentions "looking like a postcard from 1971", referring to Aqualung.
Hares/rabbits were always in abundance in Tull imagery: "The Hare Who Lost His Spectacles", the columns about "Do Not See Me Rabbit" and "non-rabbits" in the newspaper of Thick As A Brick, the line, "you're a rabbit on the run" in "Skating Away On The Thin Ice Of The New Day", the band wearing rabbit suits onstage...
Fall Out Boy's "What a Catch, Donnie" has lines from several of their songs ("Grand Theft Autumn", "Sugar We're Going Down", "Dance, Dance", plus others) sung in the background during the third stanza.
Pink Floyd's The Wall has a few of these. One of the most obvious is "Young Lust's" borrowing from "The Nile Song," an earlier tune, but there are others, including a sound effect in "Is There Anybody Out There?" mirroring one from "Echoes."
The Division Bell is filled to the brim with musical and lyrical allusions to past works. "Cluster One" sounds similar to "Shine On You Crazy Diamond" (it was written as a tribute to Syd Barrett), "Keep Talking" has a synth solo similar to "Run Like Hell" and a talk-box effect similar to "Pigs (Three Different Ones)", "What Do You Want from Me" has a groove similar to "Have A Cigar", and "High Hopes" is reminiscent of "Fat Old Sun" and "Grantchester Meadows". Allusions to "the wall" coming down on "A Great Day For Freedom" are by Word of God, not about The Wall, nor Roger's Berlin "Wall" concert, but it can be easily interpreted that way.
Roger Waters has used an inflatable pig or two in The Wall tour and solo concerts post-Animals. For a few recent solo tours, he scrolled political/social messages (or anti-George W. Bush screeds) on the pigs.
One of Hannah Montana's earliest hits is called "Life's What You Make It". The chorus of a Miley Cyrus song from 2009, "The Time Of Our Lives", has the line, "Life is only what you make it, now."
The verses of "See You Again" have "I knew you were something special", while the chorus "He Could Be The One" by Hannah Montana has "he's got something special". "Another line of "See You Again" has "I have a heart that will never be tamed". A song and album called Can't Be Tamed came out two years later.
Tony Banks plays an electric grand piano part with the same over-the-hand technique he developed on a few of the track on The Lamb Lies Down On Broadway for "No Reply At All".
The lyrics to the "Willow Farm" section of Supper's Ready refers to the "fox on the rocks" (the album the song was on was called Foxtrot.) and "the musical box". "The Musical Box" was a track from Nursery Cryme.
The end section of of Supper's Ready has the line, "There's an angel standing in the sun". Phil Collins sang the line, "There's an angel standing in the sun, free to get back home" in the end of "Los Endos" as a tribute to Peter Gabriel in their A Trick Of The Tail album.
The Gabriel-era song "Dancing with the Moonlit Knight", from Selling England by the Pound, features the line "'Paper, late!' cried a voice in the crowd," which later served as the inspiration for the Collins-era song "Paperlate."
Emilie Autumn's song Swallow has the line "I'm not a fairy, but I need/more than this life, so I became..." referencing her Enchant era where she performed in fairy wings.
In a particularly meta form of the trope, the Dresden Dolls song "Backstabber" has the line "And don't tell me not to reference my songs within my songs."
Knife Party's "Centipede" opens with "Giant tropical Centipedes share their territories with Tarantulas." A nod to Tarantula by Pendulum.
Ben Lee's song Into the Dark has the line, "I was one of those breathing tornados", alluding to his earlier album Breathing Tornados.
Pearl Jam's Greatest Hits Albumrearviewmirror opens with the first song on their debut album, "Once", and ends with the song they usually close shows with, "Yellow Ledbetter".
This is literally half of The Hold Steady's lyrics, and a solid amount of their appeal.
In the Legends & Diamonds song "Running Out Of Time" Lamar raps "Too many nights, I tried to make it shine, then I tried to fly, but it didn't work", referencing his three solo hits.
In NOFX's song "Now for Something Completely Similar", the lyrics mention the "blatant similarity" to Linoleum, referencing the similar sound to that of their earlier work.