The Police quote themselves between albums with the line:
“Do I have to tell the story, of a thousand rainy days since we first met?
It’s a big enough umbrella, but it’s always me that ends up getting wet.”
Which appears on Every Little Thing She Does Is Magic from Ghost in the Machine, and then again on My God from Synchronicity.
David Bowie’s song Space Oddity has engendered many references to an astronaut named Major Tom, both in his own later song Ashes To Ashes and in another early 80s New Wave hit (which Google tells me was Peter Schilling’s song Major Tom) and other songs I know I’ve heard…
There’s a Wikipedia article on “Major Tom”, in fact, which is pretty neat. For a while as a youngster I wondered if it was all based on an actual historical figure.
I suppose “thematic character reference” is not the same as “quoting”, though, so in the spirit of the OP I will also submit:
Counting Crows, A Murder of One, which quotes a traditional counting rhyme: “One for sorrow, two for joy; three for a girl and four for a boy; five for silver, six for gold; seven for a secret, never to be told”. (Iffin you don’t already know, I’m sure you can guess what is traditionally counted in this manner.)
Thank you for that! You’re immortalized. I did a minor correction on your albums. I appreciate the help!
“If you want to kiss the sky, better learn how to kneel”
Bono’s response to Jimi.
“You Could Have Both” by The Long Blondes references Morrissey’s “My Love Life” with the lines “Who was it who sang/ ‘I know that you love one/ So why can’t you love two?’” It’s not an exact quote, but it’s close.
Belle & Sebastian do this a lot. All I can think of off the top of my head are “He dances in secret, he’s a part-time punk” from “The Blues Are Still Blue” (references “Part-Time Punks” by Television Personalities) and “L-O-V-E love, it’s coming back” from “Legal Man” (referencing Orange Juice’s version of Al Green’s “L-O-V-E”).
Interesting…I never noticed the change. But then, I’m not much of a Rush fan.
From Dr. John’s Right Place Wrong Time:
Just need a little brain salad surgery
HA! To check I searched… Emerson Lake and Palmer’s 73 album was nicked from the Dr. John song. I thought it was the other way around. 
The OP mentions Joni - in Chinese Cafe she sings almost a verse of ‘Unchained Melody’ and in ‘In France They Kiss On Main St.’ she sings
‘Downtown in the pinball arcade
with his head full of pool hall pictures and songs from the hit parade
he’d be singing ‘Bye Bye Love’
while he’s racking up his free plays
Let those rock and roll choirboys come and carry us away’
Ah, Joni.
MiM
I must also confess to having done it myself. Lots of times. In the song ‘I.S.T.I…’ I even quoted ‘In France they kiss…’
One that I know for sure is not a cover and where the reference is to a song in english:
Chanel, Cocaína y Dom Perignon (Loquillo y los Trogloditas) includes the lines
no nací en los USA,
nací en el Clot
(I wasn’t born in the USA, I was born in Clot*)
OK, let’s end this whole Rush thing now.
Built to Spill, “You Were Right”
You were right when you said that all that glitters is not gold
You were right when you said all we are is dust in the wind
You were right when you said we are all just bricks in the wall
and manic depression’s a frustrating mess.
You were wrong when you said everything’s gonna be all right.
(goes on to explain that you can’t always get what you want, that a hard rain’s gonna fall, that we’re still running against the wind, and life goes on after the thrill of living is gone. BUT you were wrong when you said that everything’s going to be all right. Cute song.)
Nava, every time you mention Loquillo y Trogs, I crack up and smile. There is one American out there who knows what you’re talking about. I need to dig those tapes out (now I have that song, done to the tune of some 50s pop song, but about nude elephantine German sunbathers in my head).
I know most of this board has an irrational hatred of country music, but Kenney Chesney’s I Go Back is basically one long song reference.
I stand corrected. Sublight, has given the correct citation that I was trying to come up with yesterday.
Queen also had a song called Nevermore(which is awesome BTW) on Queen II.
Springsteen’s “State Trooper” also quotes Chuck Berry’s “You Can’t Catch Me,” with references to the “New Jersey turnpike” in the “wee, wee hours.”
Bob Dylan’s Sara
Staying up for days in the Chelsea Hotel
Writing “Sad-Eyed Lady of the Lowlands” for you.
Nope, what?
Crows.
And another Dylan reference - Jimmy Buffett’s “My Whole World Lies Waiting Behind Door Number 3” quotes “Do you want to make a deal?” from “Like a Rolling Stone.”
Destroyer’s “The Sublimation Hour” contains the line “until this phony Beatlemania has bitten the dust,” quoting The Clash’s “London Calling.”