Procol Harum’s “A Whiter Shade of Pale” has a shortened radio version, with a pretty obvious fade. Unfortunately, before the Internet made the issue moot, it was very rare to hear the full version.
Edited to add: I think my example counts. Both versions were played at times, even though the shorter one was much more common. Apologies if it doesn’t really fit the OP’s criteria.
There are two versions of “Let’s Get It On” by Marvin Gaye: the single version,which is the one most people have heard, and thealbum version which is about one minute longer and has an additional verse that I suspect was too racy for most Top 40 radio stations in 1973. Today, most oldies stations still only play the short version but, on occasion, I have heard the long version.
“Hungry Like the Wolf” by Duran Duran has an identical story, I believe. I just wish I could remember which album it was on…
Clapton’s Layla, with or without the whole slower, instrumental end part.
The first example that comes to mind for me is Boston’s “More Than A Feeling”. The verse that starts “So many people have come and gone…” was cut out for AM radio.
Which reminds me of the next track(s) on the album, “Foreplay/Long Time”. When that album came out, I was in junior high, and we didn’t know that “foreplay” was anything other than a song by Boston. 
:smack: :o
So-called “Oldies” stations have almost completely abandoned playing any music from the 60s except for a few very obvious artists that can’t be ignored. (50s rock ‘n’ roll disappeared several years earlier.) They now tend to play mostly 70s and even 80s stuff.
Back when they were playing 60s stuff, though, they were notorious for ignoring the way the songs were actually heard on Top 40 radio when they were current, because they were all on FM and wanted to play stereo versions…even though stereo mixes were often quite different from their original mono single mixes.
In some cases, this even resulted in them playing completely different recordings of the song in question. The most notorious example is The Animals’ “We Gotta Get Out of This Place.” An alternate (and IMO, vastly superior) performance of the song was accidentally sent to the United States, and that’s what became the hit. But on Oldies stations that still play it now, you almost inevitably hear the inferior version that was a hit everywhere else in the world.
The reason I’m bringing this up is that Oldies stations (when they were playing 60s stuff) often played the album versions of hit singles instead of the singles mixes. While I’m usually against this practice, there are two cases I can think of in which I’m glad they do: “Get Together” by The Youngbloods and “Suite: Judy Blue Eyes” by Crosby, Stills and Nash. The single versions of each were both horrendous butcher jobs, cutting out key passages of the songs all in the name of getting them to 3:00 or below.
A similar hack job was performed on Cream’s “Sunshine of Your Love.”
I’m not aware of any long version of “A Whiter Shade of Pale” other than the unreleased stereo version, which didn’t come out until the 30th Anniversary Anthology. Certainly the version that came out on Procol Harum’s debut album in the U.S. was identical to the single release (outside of being in fake stereo).
I’ve seen a live version of the song performed with an extra verse that wasn’t on the original single, but I don’t ever recall a longer version being played when the song was current…unless there was something else out in the UK I wasn’t aware of.
The station I listen to has a version of “Lyin Eyes” that cuts out the verse where she mets her lover across town. Which is kind of a major point in the song since that’s what she’s lying about!
Ditto “And When I Die.” The short version cuts out the honky-tonk piano after the second verse.
Santana’s Black Magic Woman.
The hard-driving instrumental section at the end is so awesome, that, during the filming of the El-Train race in The French Connection the director had the stunt driver play it on tape in the stunt car during the run to get him in the proper “mood”.
“Do You Feel Like We Do?” usually loses the whole middle, catching only a bit of the band solos and the talkbox.
I’ve counted as many as five mixes on the radio.
Chaka Khan’s " I Feel For You" has two versions, one of which excludes the Stevie Wonder harmonica sampling from “Fingertips Parts 1&2”. That version is on the played most often on pop radio,while R&B stations will often play the entire song.
I remember when “Money For Nothing” by Dire Straits came out stations played the full album version, which included the verse about the little faggot with his earring and his makeup. Now, it’s more common to hear the single edit, which omits that verse, even on radio stations that originally played the album version.
I would have put it the other way around: the monolgue “Late Lament” is a separate song, but it is part of the same track on [the album on which the song appears](Days of Future Passed - Wikipedia).
(Oh, and it’s “Nights,” not “Knights.” Are you really picturing knights in white satin?)
I’ve heard it mondegreened as “Knights in White Saddles.”
The Top 40 radio version of Elvin Bishop’s “Fooled Around and Fell in Love” omits the entire second verse and part of the instrumental break. Unfortunately, the short one is still the version played on oldies stations today. However, I have noticed it’s easier to find the long version than the short version on You Tube.
Steppenwolf’s “Magic Carpet Ride” (1968). Short version was on AM radio. Long version was on “Underground Radio” on the FM dial.
Jack FM was playing “November Rain” (Guns N’ Roses ). They chopped it off, fading it right before the Slash-jumps-up-on-the piano-and-blows-you-away power jam. :eek:
I don’t remember the Fabulous Freebirds using it as their entrance music very long. Most of the time they used “Badstreet”.