The New Style off Licensed to Ill, I only know cause it’s my favorite song on that album.
I can’t believe nobody’s mentioned Frank Zappa yet. More examples than I can count.
And while not exactly musically self-referential, I’ll mention the new Wilco album, which is titled “Wilco (The Album)” and has a song titled “Wilco (The Song)”.
At the end of Wilco’s “I am Trying to Break Your Heart”, Jeff Tweedy sings, “I’m the Man Who Loves You”, another song on the album.
“It’s a big enough umbrella, but it’s always me that ends up getting wet.”
Originally from “Every Little Thing She Does is Magic” on Ghosts in the Machine, shows up in “O My God” on Synchronicity… and other songs that Sting has done as a solo artist.
“Every breath you take.”
Originally in the song of the same name on Synchronicity, quoted on “Love is the Seventh Wave” on Sting’s Dream of the Blue Turtles.
Enya’s “On my Way Home”, from The Memory of Trees, has a sample of one of her earlier songs in the background, but I can’t remember what the other song was called.
It also features the line “Met a girl called Lola…”
And their song “The Road,” essentially a look back over their long career, includes the line “They’re just dedicated followers of fashion who like putting down all the well-respected men who came dancing…”
Veruca Salt: “I told you about the Seether before…”
The Who: “To the sound of ol’ T-Rex…and Who’s Next…”
Digital Underground: “I sang ‘Do What You Like’ and in case you missed it I’m the one who sang ‘just grab him in the biscuits’”
Thinking outside the box (CD case?) how about Jethro Tull’s Strange Avenues off of Rock Island?
They’re referencing their 1971 album cover for Aqualung, which had a homeless man on it.
The Lamb Lies Down on Broadway cites itself near the end, but that might be a reprise than what you’re talking about here.
The Beatles’ Glass Onion contains the self-referential line “I told you 'bout Strawberry Fields”
Piggybacking Shoeless’s idea: both Black Sabbath and Iron Maiden have eponymous songs or eponymous albums.
Do Metallica’s “Unforgiven” and “Unforgiven II” count?
Are you aware there’s an even crappier “Unforgiven Three?”
The original versions of Traffic’s Dear Mister Fantasy album, starts out with the song “Paper Sun.” You could hear bits of “Paper Sun” between the other songs, and the final song was titled “We’re a Fade; You Missed This,” which is a final coda to “Paper Sun.” Most CDs drop all this and tack “We’re a Fade” onto “Paper Sun.”
Steve Miller often referred to older song titles in his songs. “The Joker,” for instance, begins with “Some call me the Space Cowboy/Some call me the Gangster of Love.” “Space Cowboy” and “Gangster of Love” were earlier Miller songs.
He starts out “Space Cowboy” with the line “I told you 'bout living in the U.S. of A./Don’t you know that I’m a gangster of love.” That refers to “Livin’ in the USA” and “Gangster of Love.”
I also believe there was one song that name checks “Space Cowboy,” “Gangster of Love,” and “The Joker.”
In Mozart’s opera Don Juan, during the dinner scene, Don Juan has hired an orchestra to play music, and one of the tunes they play is from Mozart’s opera The Marriage of Figaro. IIRC Leporello (the servant) says something like “oh yes, I know that tune well.”
Actually, I wasn’t, but I like it! Another reason to pick up Death Magnetic one of these days. Haven’t gotten around to it yet…
I don’t think this is really what the OP is looking for. Tommy and Quadrophenia are not just collections of songs written around the same time, the albums were written as “rock operas” and are meant to be taken as a whole. I wouldn’t call for instance the repetition of “See me, feel me…” in Tommy a case of a band citing itself, it’s just a repeated theme within one larger musical work.
That said, The Who did cite themselves on plenty of other occasions. RealityChuck already mentioned that there were earlier Who songs that Pete Townshend borrowed from when writing Tommy. One he didn’t mention was “Glow Girl”, a pre-Tommy song about a woman who dies in an airplane crash but is apparently reincarnated at the end – the song concludes with repetition of the line “It’s a girl, Mrs. Walker, it’s a girl!” Tommy begins with the (apparent) death of the main character’s father, Captain Walker, in an air crash, and the birth of Tommy is announced with “It’s a boy, Mrs. Walker, it’s a boy!”
The 1978 song “Sister Disco” uses the phrase “deaf, dumb, and blind” which is/was a fairly common expression but in the context of a Who song is also evokes their famous “deaf, dumb, and blind boy” hero Tommy.
The Aqualung album would be a borderline case of this. Cross-Eyed Mary name-checks Aqualung, although the band denies that the album is a theme album.
Deep Purple’s “Hungry Daze” includes the line, “We all came out to Montreux… but that’s a different song.”
The Byrds’ “Love That Never Dies” features the line, “Throw a dime to the Tambourine Man, and kiss all the horses good-bye.”
And the Guess Who had an autobiographical song called "When the Band Was Playing ‘Shakin’ All Over.’ "
The Hold Steady have a song on Separation Sunday, “Cattle and the Creeping Things” with this line-
“Silly rabbit. Tripping is for teenagers. Murder is for murderers6. And hard drugs are for bartenders. I think I might have mentioned that before.”
This is a reference to a line from “Certain Songs” from their previous album.
“Hard drugs are for the bartenders and the kitchen workers and the bartender’s friends.”
Off The National’s Boxer, Slow Show ends with a callback to 29 years off their first ablum, The National.