“No Man’s Land” aka “The Green Fields of France” by Eric Bogle and others mentions “Flowers of the Forest” and “The Last Post”. Some covers mention “The Death March”.
He also used lines referring to “beat the drum slowly” and “play the fife lowly”, which were also used in “Streets of Laredo”. I suspect those lines are much older than SoL.
nm
Tom Petty’s “Runnin’ Down a Dream”:
It was a beautiful day, the sun beat down
I had the radio on, I was drivin’
Trees flew by, me and Del were singin’ little Runaway
I was flyin’
Refers to Del Shannon’s 1961 hit “Runaway”
“June” by Spock’s Beard:
Then the sun came up on a sleepy day
And never went down at night
And the crowd kept on singin’ Waste Away
but it just didn’t feel right
“Waste Away” is a song from their previous album.
It was written and recorded by Eric Bogle, and covered by the Pogues
This song’s from the early years of the twentieth century, and Dylan’s version was a poor cover, IMHO.
Speaking of Dylan, Roll On John from his latest album is a tribute to John Lennon, and references several of his songs.
My 2 favorites are:
The song “Long May You Run” by Neil Young references The Beach Boys “Caroline No”
Maybe The Beach Boys
have got you now
With those waves
singing “Caroline No”
The other is the song “Great Leap Forward” by Billy Bragg.
It references “All The Way To Memphis” by Mott The Hoople by taking the line “Its a mighty long way down rock’n’roll.” But Billy adds the line “From Top of the Pops, to drawing the dole.”
“Standin on a corner in Winslow Arizona
And I’m quite sure I’m in the wrong song…”
Rhett Miller has an hilarious one. I’m going to have to paraphrase, because I don’t recall the name of the song to look it up. Something like, “Makin’ lovin’ out of nothin’ like the Air Suppliers said”.
Air Suppliers. 
<snip>
Thanks!
I just remembered, “Down In It” by Nine Inch Nails:
Rain, rain go away
Come again some other day
Sweet Home Alabama
Play that dead band’s song
Turn those speakers up full blast
Play it all night long
Warren Zevon-“Play it All Night Long”
The Traveling Wilburys’ “End of the Line” references “Purple Haze.”
“Sweet Home Alabama” references two Neil Young songs- “Alabama” and “Southern Man”. “Alabama” is just as scathing as the other.
Also referenced in I’m Not Sleeping by Counting Crows.
Mott the Hoople referred to their earlier song “Half Moon Bay” in “Driving Sister”: “Eight-track machine playing ‘Half Moon Bay.’”
While not in the lyrics, Mathew Fisher clearly references “A Whiter Shade of Pale” musically in “Going for a Song” and is singing about playing it.
“We Didn’t Start the Fire” by Billy Joel mentions “Rock Around the Clock.”
How about a link to the lyrics for “Rocket” from Def Leppard? Pretty much all they do in that song is mention other songs.
Here’s the Wiki that sums up all the references.
Included, among others, are songs by the Rolling Stones, Elton John, the Beatles, Queen, and Bowie.
Country-folk songs use that trick. Dolly Parton:
Jonathan Edwards’ “Honky Tonk Stardust Cowboy”:
“Going Back to Harlan” by the McGarrigle Sisters is full of folky references…
My Whole World Lies Waiting Behind Door Number Three quotes "Like a Rolling Stone
though when I heard Steve Goodman sing it, I swear he sang “make a deal”.
“The Legend of the USS Titanic” by Jamie Brockett references Dylan’s 115th Dream
“Deadbeat Club,” by B-52s refers to “96 Tears,” by ? and The Mysterions.
That’s reminded me of another good one - from “Desperados Waiting For A Train” by Guy Clark.