Golden Slumbers" / “Carry That Weight” / “The End” - The Beatles
“Foreplay” / “Long Time” - Boston
“We Will Rock You” / “We Are the Champions” - Queen
“Heartbreaker” / “Living Loving Maid (She’s Just A Woman)” - Led Zeppelin
“Speak To Me” / “Breathe” - Pink Floyd
“On the Run” / “Time” - Pink Floyd
“Any Colour You Like” / “Brain Damage” / ‘Eclipse" - Pink Floyd
“Travelin’ Man” / “Beautiful Loser” - Bob Segar
“Space Intro.” / “Fly Like an Eagle” - Steve Miller Band
“Eruption” / “You Really Got Me” - Van Halen
“Waiting For The Bus / 'Jesus Just Left Chicago” - ZZ Top
“Your Move” / “I’ve Seen All Good People” - Yes
“The Load-Out" / “Stay” - Jackson Browne
“Need You Tonight” / “Mediate” - INXS
“Lovin’, Touchin’, Squeezin’” / “City of the Angels.” - Journey
“Falling In And Out of Love” / “Amie” - Pure Prairie League
'Don’t Want You No More” / “It’s Not My Cross to Bear” - The Allman Brothers Band
“No Sugar Tonight” / “New Mother Nature” - The Guess Who
“Fat Bottom Girls” / “Bicycle Race” - Queen
"Lights’ / Feelin’ That Way" - Journey
I would only add Alan Parson’s “Sirius”/ “Eye in the Sky”.
Most of them are in that sequence on the original record. I was actually confused about the Heartbreaker/Living Loving Maid sequence for years on end until I commented about my confusion here. Come to find out, they’re that way on the record. I’d had 3-4 copies of Led Zep II on tape, but had never owned it on album, so I wasn’t familiar with that sequence.
With Alan Parson’s “Sirius” being an instrumental and being so short (under 2 minutes), I never realized that it wasn’t just an intro to “Eye in the Sky” until bought the song(s).
BOTR is one song with some distinct parts. So is Uncle Albert/Admiral Halsey. Paul apparently had some song fragments that he liked and thought they went well together.
Devo had a few of these…
Timing X-Clockout
Smart Patrol-Mr. DNA
Gut Feeling-Slap Your Mammy
I don’t think I’ve ever in my life heard “Fanfare–Fire Poem” played on the radio.
The Guess Who example in the OP is not two separate songs. It’s one track with two melodies sung over the same (minimal) chord pattern, first one, then the other, and finally both together in counterpoint.
I think all the listed examples are songs that come one after another on the album on which they appear. Technically, any songs that appear one after another on an album are “often played one after another,” assuming the album gets played very often—but I assume you meant “often gets played” on the radio, or something like that.