Top 10 Possible Features in a Non-Standard Song Structure

The most common song structure is:

Verse
Chorus

Verse
Chorus

(Bridge
Solo)

Chorus
Chorus

But there are songs with very different structures - for example, multi-part songs like Bohemian Rhapsody where for the listener may be hard to understand what's happening in that (what is the verse? what is the chorus? what is this???)

But Bohemian Rhapsody structure isn't the only non-standard song structure.
The Top Ten
1 No chorus

This structure is more spread in metal. These songs are called "multi-part songs" because they simply go from part to part - a series of related but discrete musical sections strung together. And no part is repeated so there's no chorus despite the songs are usually longer than your average song.
Songs without a chorus are harder to write and also harder to be "digested" by the listener. Chorus is the hook and when you have no chorus you have to be more focused while listening in order to understand what's going on (in terms of music and not lyrics/story).
Chorus is the candy for the ears we all wait for but some songs have no candy. It took me some time but currently I completely enjoy songs with no candies. And even songs with too many candies began to annoy me.
Songs with no choruses:
Queen - Bohemian Rhapsody
Iron Maiden - Hallowed Be Thy Name
Megadeth - Holy Wars...The Punishment Due
Iron Maiden - Phantom of the Opera
(for more, check out the list - Top 10 Metal Songs Without a Chorus)

2 No verses

Is it possible? , you may ask. Oh yes. This is the opposite of "No chorus" - here you get only choruses, I.e. candies. For this reason, this song structure is very good for children songs.
Example: Love Me Do by the Beatles.
This song has no verses (by strict definition) and the song structure is:
- Instrumental intro (over partial chorus chords)
- Chorus
- Chorus
- Bridge ("Someone to love..." - this is a bridge because it's different from the main chord pattern)
- Chorus
- Instrumental, part 1 (over bridge chords)
- Instrumental, part 2 (over unique pattern)
- Chorus
- Fadeout (over chorus chords)

3 Song starts with the chorus
4 Guitar solo in the intro

Usually the guitar solo is somewhere in the middle of the song but not in these songs:
Scorpions - The Sails of Charon (1977)
Annihilator - The Trend (2010) [even 2 solos in the intro]
Slayer - Captor of Sin (1984 demo). Ha! It even starts with the solo! And the riff comes after the solo!

5 Different verse structures

Thanks for adding this, romanempire249, and the example with the Blind Guardian song - The Throne is one of my favorite songs by them. The Throne has a chorus but the three long "verses" have different music and structure so the song doesn't get repetitive although it's 8 minutes long. Pure genius.
Blind Guardian songwriting is unique and is non-standard for the most part - many of their song structures are like a puzzle. Off the top of my head - Curse My Name and The Holy Grail are pretty odd, too, but I love them.

6 No instrumental intro

Instrumental intros prepare the listener for the tone and mood of the song. But there are songs where the singer just starts singing. Because most of the songs we know have some instrumental intro, at least for 5 seconds, such songs surprise the listener (which can be super cool though).
Queen - Bohemian Rhapsody
Pink Floyd - Another Brick In the Wall, Pt. 2
Bon Jovi - You Give Love a Bad Name
Green Day - Basket Case
(for more, check out the list - Top 10 Songs With No Instrumental Intro)

7 Pre-chorus

Blind Guardian's The Throne (2015) is like 8 minutes long and has 3 choruses and 3 pre-choruses. When I first heard the song and its first pre-chorus, I thought "what a great chorus". When it finished and I heard the real chorus, I realized that the song has pre-choruses.
The chorus starts with "We must serve the fire...".
These are the three pre-choruses before every chorus (lyrics aren't absolutely the same but music is):
Pre-chorus 1
I've come to tell you once more
Don't let him break this seal
But let me tell you once more
Peace shall come
Pre-chorus 2
I've come to tell you once more
It's me, I hold the key
But let me tell you once more
Peace shall come
Pre-chorus 3
I've come to tell you once more
As I will now reveal
But let me tell you once more
Peace is gone

8 Song starts with a guitar solo

This is really crazy but Slayer did it (Captor of Sin, on their 1984 demo). The solo is followed by the riff.
One of my favorite Slayer songs.

9 Guitar solo in the outro

Guitar solo in the outro happens more often than solo in the intro but it still deviates from the rule: solo in the middle of the song. Example: Primal Fear - The Man (That I Don't Know). The song has 2 solos but I like better the 2nd, outro solo.

10 Song starts and ends with the chorus, but there are no choruses in between

Example:
Joanna Newsom - The Book of Right-On (2004)
Between the starting and the ending chorus there are only alternating verses and bridges. I would call this structure a "sandwich song structure".

The Contenders
11 Bridge / interlude instead of a guitar solo

Guitar solos are usually expected in rock/metal songs because the guitar solo became an important part of the common rock song structure.
And when there's no solo the listener is either surprised or doesn't notice the absence of the solo because some songs are amazing even without guitar solos. Here are several great songs with no solos - oddly enough, some of them were written by famous soloists who often put 2-3 solos in a song but not here:
Deep Purple - Perfect Strangers
Judas Priest - Breaking the Law
Annihilator - Human Insecticide
Demons & Wizards - Crimson King
(for more, check out the list - Top 10 Greatest Metal Songs With No Guitar Solo)

12 Multiple entirely different sections of a song

Yes, what about no structure at all? I feel like musicians feel it is compulsory that a section in the song should happen more times, either musically or lyrically. There should be much more songs that just build up without repeating melodies and lyrics. Listen to the commercial album by The Residents, all 40 songs are just 1 minute without any repetition and they're still full works of music.

I didn't add this item because it's the same as "No chorus", or very similar to it.
As I explained in "No chorus", if a song is multi-part (all parts are different), it has no chorus - chorus is something that has to be repeated at least twice.
So the songs from "No chorus" can be examples here as well:
Queen - Bohemian Rhapsody
Iron Maiden - Hallowed Be Thy Name
Megadeth - Holy Wars...The Punishment Due
Iron Maiden - Phantom of the Opera

13 No lyrics

Instrumental music have no lyrics. And without lyrics we can't talk about verses and choruses. Many people don't count instrumental songs for "songs" because they think a song should have lyrics. What do you think about that?
Do you need lyrics to understand and enjoy music?

People, it's not only about instrumentals, Alcest's 2016 album Kodama has multiple tracks where all the "lyrics" are made-up gibberish which they thought fitted the music

14 Song ends with a verse

Example: Blind Guardian - The Bard's Song (In the Forest).
After the 3rd verse there is no chorus and the song ends with the 3rd verse - if these can be called "verses" in the strict sense because they aren't absolutely the same. But the song has a chorus so the rest of it must be "verses".
Ending this song with a verse is not everything:
the first 2 verses aren't the same but are very similar. The 3rd one is too different and appears only once in the song - it sounds like a bridge to me. But if the song ends with it, it's a bridge to what? (because a bridge connects 2 points).
A possible answer would be: bridge to the next song on the album that is related to this one: The Bard's Song (The Hobbit).
Whether it's a verse or a bridge, the end of this song is unusual. And after the 3rd verse (or bridge? ) there's no intstumental outro or something like that. But somehow the song sonds finished.

15 Pre-chorus in the middle of the verse and not in its end

By definition, if a song has a pre-chorus, it's the last part of the verse that is right before the chorus. But who put a pre-chorus in the middle of the verse? Blind Guardian, that's who (The Holy Grail). Blind Guardian rarely do something by the rules. Besides, there's no pre-chorus in the 3rd verse. Oh, and these pre-choruses are with different lyrics...
Example: Blind Guardian - The Holy Grail
The chorus starts with "There on the battlefield..."
Pre-chorus 1:
"Don't call it hopelessly insane Oh Oh Oh
I go and grasp the grail Oh Oh Oh
But in a graceful way Oh Oh Oh
Illegally, my aim
The grail will cross the border now"

Pre-chorus 2:
"So after all, in vain Oh Oh Oh
I've met him and found the grail Oh Oh Oh
Cause in a skillful way Oh Oh Oh
I'll change to keep alive
Eternal lie, I'll be the one"

16 Many segments with different tone

I didn't add this item but this may be the same as "Multiple entirely different sections of a song", which is very similar to, or the same as "No chorus".
But I don't know what the person who added this had in mind so I can't be sure.

17 Only one verse

Cro's "Unendlichkeit" (my favorite song of 2017) starts with the chorus, then a verse, then another chorus, a bridge, and then an instrumental outro. There are two different versions with different verses, but the structure is the same.

18 Rap verse by a guest artist instead of a bridge

This was most common in the early to mid 2000s.

19 First two verses, then two choruses
20 Multiple bridges
21 Three verses and then chorus repeated multiple times

No, it's worse than the standard structure in the description. These are the kind of songs that run for 5 minutes but have enough ideas to fill 2 minutes.

22 Solo after the first chorus and before the second verse

As heard in Scissor Sister's "I Don't Feel Like Dancin'". Was a synthesizer solo though.

23 Starts with a chorus, ends in a verse
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