Long songs that tell a story

Arlo Guthree's Alice's Restaurant has you covered. I play it every Thanksgiving.
- So does my family! I think it's a New England thing.

A bunch of stuff in the classical realm fits that bill, holst's the planets, a bunch of operas some with words some without many in other languages you wouldn't understand. One modern song with words that I want to be in these comments is Albuquerque by weird Al. I'll also mention Maggot brain by funkadelic
- I had forgotten about maggot brain, such a great song! Thanks for reminding me.
- Beethoven's Symphonies come to mind. His 5th and 6th symphonies really do tell stories and are very engaging.
  
  I actually had a music teacher that used the 5th as an example. It's a story of dundundun duuuun

Most of Coheed and Cambria's albums follow along with a graphic novel written by Claudio, the lead singer. I've never read them and don't know the story, but if you listen to an album start to finish, you can tell that it's more than just lyrics.
- The Coheed and Cambria comics are awesome. They're hard to get your hands on, after Umbrella Academy got popular, but worth it.

The Decline - NoFX
https://youtu.be/oWhy8PCuGsk
- Here you are, was definitely the first thing to come to mind.

2112 by Rush
Jesus of Suburbia by Green Day
And almost anything by The Mars Volta
- Green Day actually has quite a few, it would really be worth listening to their entire discography. They started out with a lot of teenage love songs (angst and longing) and over the years it faded but love is still a very common topic for Green Day!
  Most recently, Father to a Son, from the album Saviors.
- I'm not sure anything with Omar Rodriguez-Lopez can be said to have a narrative. You'll go on quite a journey, but it's not really a story.

Dating myself a bit here, but Meatloaf's Paradise By The Dashboard Light, and Billy Joel's Scenes from an Italian Restaurant are 2 that need to be on this list.

Alice's Restaurant by Arlo Gurhtie. Actually, just about anything by Arlo Guthrie and his dad, Woody.
Indian Ira Hayes by Johnny Cash. It's not very long, but a poignant story that shouldn't be forgotten.

the repeat itself part is a bit tough with music. music is sorta a repeating sequence of notes and usually even the most complex will have some sorta of repeating element. That being said the band jethro tull has many songs that are story and two are album length. Pretty much all of them have at least a significant meaning but most are basically stories. The one that I think would most meet your criteria is passion play https://www.youtube.com/watch?v=0XrlWumWbUU&t=241s&pp=ygUMcGFzc2lvbiBwbGF5 side one and https://www.youtube.com/watch?v=FUyIhIhf3A4&pp=ygUMcGFzc2lvbiBwbGF5 being its from the days of records they needed a way of linking the two sides. Curiously in this one did it with a unrealted story that just sorta starts getting told in the middle of the song. You may not like that. Its other album length song, thick as a brick https://www.youtube.com/watch?v=ldXdnZtTWp8&pp=ygUQdGhpY2sgYXMgYSBicmljaw%3D%3D https://www.youtube.com/watch?v=GTWQv8RsI6s&pp=ygUQdGhpY2sgYXMgYSBicmljaw%3D%3D , is a story but its not as straight forward and more flowery being a bit more about life and society and the struggles of the individual. Its transition is really neat as the music blends with this wind sound which fades and then starts back up on side B. Its a great transition. If I get some time I will do a list of some other songs along with the idea of the story but they are not super long although most of their songs are not exactly short.
- First I have to mention that there was an overlay of one of the shortened versions (20 or so minutes) of thick as a brick with a silent black and white short film called "an occurrence at owl creek bridge" but I can't find it. Likely it was taken down. But it is one of the best overlay music to film type of things I ever experienced.
  While goign through I realized how hard it is to say something has become a proper story and im not sure all of these are. There is a sort of tale around most all tull songs but many sorta walk the line between story and just sort of meaning. Also I likely lack some context to understand the story from some.
  "For Michael Collins, Jeffrey and Me" - this is about the guy who stayed in the lunar module on the first moon landing - 4mins "Aqualung" - about a homeless man - over 6 mins "cross eyed mary" - about a teenage prostitute - 4mins "Locomotive Breath" - shorter song about the plight of life - 4minish "Wind-Up" - about why worship of a god is necessary - 6mins "sweet dream" - if the collection of music videos made in a dvd called slipstream is to be believed its about a vampire seducing a girl. - 4mins "The Witch's Promise" - boy being seduced by witch - almost 4mins "Minstrel in the Gallery" - farciful story of a bard getting it over on the man - 8mins "Baker St. Muse" - adding this in because I feel its the songs the bard from minstrel in the gallery might of sung. Its one song that is sorta 4 songs and goes for 16mins "we used to know" - this song is sorta a meloncholy nostalgia for the band when it started and those not with it and sorta works as a brief story of being in a band before and after success "Quizz Kid" - about the game show cheating scandal from the 1950's - 5mins "Crazed Institution" - about being famous - just under 5mins "From a Dead Beat to an Old Greaser" - exactly as it sounds about generational divide - 4mins "Too Old to Rock 'n' Roll: Too Young to Die" - about generations sorta selling out. could be silent generation but I think its about boomers especially given its late seventies and its about where is your rock and roll spirit that defined you - 5+mins "Hunting Girl" - high status girl gets rare opportunity alone with a young nobody from the perspective of the nobody - 5mins "Velvet green" - guy trying to convince girl to take a roll in the hay - 6mins "Pibroch (Cap in Hand)" - guy walks in on cheating wife - 8mins "fire at midnigh" - guy walks home to loving wife - 2+mins "...And the Mouse Police Never Sleeps" - about cats - 3mins "Moths" - about the allure of fire - 3+mins "journeyman" - commuting home on a train - 4ish
  
  "Rover" - being a dog - 4+mins "One Brown Mouse" - mouse in a cage - 3+mins "Heavy horses" - about horses - almost 9 mins "weathercock" - man ponders the life of a weather vane - 4mins "Something's on the Move" - icequeen tale - 4+mins
  that last one is just one from the album which is sorta an enviromentalism type of album and the last form the 70's. Im going to put a few more but getting weary of the task that was at first fine so it will just be a smattering. very often the albums have a theme and are constucted in a particular way. This is one thing I hate about remix albums as it loses the very intentional construction of the album and if I ask amazon to play an album it will always choose the latest remix one. sigh
  "Working John, Working Joe" - like it sounds - 5mins "Black Sunday" - putting sunday as the worst day instead of monday. Its hard to relate now but before the 80's in much of the western world practically nothing was open on sundays - 6+mins "and further on" - not a story but seems to be a reaction to someones death and just love the emotion it conveys. very complex to me and reminiscent of "we used to know" but totally different mix of complex emotions - 4+mins "Flying Colours" - dude describing what fighting with a loved one is like - 4+ "Steel Monkey" - either a high rise steel worker or a male prostitute - 3+mins "Farm on the Freeway" - losing the farm - 6+mins "I'm Your Gun" - about being a gun - 3+mins "Down at the End of Your Road" - making it big in real estate - 3+mins "17" - nostalgia about being young - 3+mins "Big Riff and Mando" - dude steals bands guitar - almost 6mins
  ok lastly just putting a note that when the band reformed in recent times their first album "zealot gene" which was delayed by covid ended up being such a good summation of that first trump administration. The band has the strange distinction now of having musical commentary from nixon till present. One of the funny things is I associate it with the US but im sure plenty of it is more about the UK. Its amazing how close our political idiocy tends to be to each other.

I don't know about without words (and only slight repetition for effect), but I really like The Mariner's Revenge by The Decemberists.
If you want to get into older music, Der Erlkonig by Shubert is a good one.
- Came here to say Mariners revenge. Love that song.

Wreck of the Edmund Fitzgerald
The whole album Days of Future's Past by the Moody Blues (with the London orchestra)

Doesn’t a song have words by definition?
If you’re looking for musical compositions, I’d say Schubert’s Death and the Maiden quintet or Grieg’s In the Hall of the Mountain King.
- Thanks, English is not my best skill, so yeah, just music
- Not if you're singing in scat

Interstellar 55555
- Was going to recommend this too
- So good

Slick Rick - Adults Only
EDIT: I haven't had coffee and missed the "without words" part. Sorry, but enjoy regardless.

2112 by Rush

Mastodon's Crack the Skye tells a story about Astral Travel and weaves in references to Rasputin
https://www.heavyblogisheavy.com/2016/02/15/prognotes-mastodons-crack-the-skye-part-i/
Fat Cats, Bigga Fish tells a story about the broader effects of class struggle
https://m.youtube.com/watch?v=pios2RY2G_Q

Vivaldi's Four Seasons.
Metallica's
To Live Is To Die.
Orion

Give a listen to "Music inspired by the snowgoose" by camel.
They were a psychedelic /progressive rock band from the UK who wanted to write an album based on a short story called The snowgoose. The author wasn't a fan, unbelievably, so they scratched the lyrics and added "music inspired by" to the album title. The whole album is a journey that I can't recommend enough!

Badger Badger Mushroom

Thick as a Brick

This question has some weird conditions on it - "doesn't repeat itself" is the most troubling one. Pi has an infinite number of sevens in it (so it repeats the same values quite often) but it's unique in its entirety - it also has infinitely long blocks that are repeated because, you know, infinity be weird like that.
I'd point you to a symphony like Vivaldi's Seasons or, if you're willing to substitute "words I can't understand" for "words" (and don't happen to speak German) Der Ring des Nibelungen. While the later does have talkie bits understanding those gives you barely any more context than the raw emotion of the music.
But, both of those (and all music that doesn't suck) relies heavily on repetition... but they're also unique overall (unless they don't have a strictly defined form aka jazz but now we're really in the weeds)
- Yeah, I don't mean that it doesn't have repeating things, I don't know how to describe this better. Just not the same thing for an hour, but flowing to different states, moods, melodies, y'know
  
  Ah that's quite fair. Vivaldi's Seasons is a lot of fun then and I might add Dvorak's Symphony for the New World to the pile as well.

Tommy is the rock opera album by the who that is all one story

I'm also ignoring the without words part to share Aesop Rock.

City Hall by Tenacious D

"The chances of anything coming from Mars are a million to one he said"
Jeff Wayne's War of the Worlds epic

Iced Earth's debut album was called Night of the Stormrider. It weaves a pretty dark tale of a mans betrayal by religion, subsequent turn to the dark side and final regrets over the course of nine tracks (46 minutes).
Queensryche's (arguably) best album Operation: Mindcrime. It tells the tale of a young malcontent who becomes involved in an underground revolution as an assassin. This is another that is not just one song, but a story that spans fifteen tracks. One of the best rock operas that was ever pulled off in my opinion.
Manowar's album The Triumph Of Steel has a first track called Achilles, Agony and Ecstasy in Eight Parts. It is essentially a telling of the tale of Hector and Achilles. It's nearly 30 minutes over the eight unique sounding parts.
Ice Nine Kills has now (2) entire albums with tracks inspired by horror movies, but I wouldn't call them long. Their song Meat & Greet would be a great example. It's a retelling of "The Silence of the Lambs".
Animals Without Leaders has a song called CAFO that I just adore. Its pretty long and although it speaks no tale, it's so sonically unique that it feels like it does. Some of those ultra technical metal bands feel like that (to me at least).

https://www.youtube.com/playlist?list=PL1CPB-gBhcNVqwY0-fWgIdjnkPeMcfFFE David Bowie narrates Sergei Prokofiev's 'Peter And The Wolf'. The narrator tells a story and the orchestra illustrates by using different instruments to play a "theme" that represents each character in the story.
For modern stories I like The Curse. It's about an archeologist that falls in love with a mummy that comes to life.
https://www.youtube.com/watch?v=gxWxiuJRApU

I figured there'd be plenty of mentions of Rush's 2112, but they have a lot of other songs that fit the bill too. The Necromancer, Fountain of Lamneth, Xanadu, Natural Science (well I guess that's more of a rant than a story), Cygnes X-1 books 1 and 2. Since you say maybe without words, La Villa Strangiato.
If you want to stick to classic prog then Yes has some songs that fit the bill too like America and Harold Land. I confess to not really understanding the lyrics of most of the rest of Yes's discography, they can be really poetic, but I think the whole Closer to the Edge album fits on it's musicality alone. The title track's a freaking journey.
Led Zeppelin has a few of these too, though musically they are a little repetitive. Achilles Last Stand, Battle of Evermore, Gallows Pole.

Not a song, but two whole "fuzz rock/metal" albums written to work as one long story: Howling Giant's Black Hole Space Wizard Part 1 and 2
The story isn't super direct, but it's about an escape ship fleeing the dying earth, crashing (Part 1) leaving one survivor, and him going on a maddened journey to become the earth wizard (Part 2).
A bit less obscure is the Protomen's Act 1 and 2, a rock opera fan fiction based off Megaman

The Hurricane by Bob Dylan
https://youtu.be/bpZvg_FjL3Q?feature=shared

Aqualung by Jethro Tull may meet your needs. If you're Will ng to flexible in your definitions the the Crane Wife cycle by the Decemberists might also fit .

Iron Maiden - Empire of the Clouds
- Iron Maiden - Rime of the Ancient Mariner
  
  Hell yeah

Its called opera.

The Wall and American Idiot always springs to mind when I think of story albums.

Avenged Sevenfold - Exist is a 15 minute song that is about the big bang all the way to Earth forming and cooling.
American Pie - Don McLean it's the history of rock and roll from the 50s through the 60s
- Cats in the cradle, has no one said this one 😭 😭 😭

These have words but might still fit the other factors:
Bohemian Rhapsody - Queen Horses - Patti Smith

Its technically an album, but the "continuous mix" of Thomas Bergersens American Dream

(maybe without words)?
In the Hall of the Mountain King by Edvard Grieg. It's not that long though.
- In the hall of the mountain king is part of the work Peer Gynt. The whole thing is about 2 hours, but there's a shorter version consisting of two suites which is about 30 minutes long. Here's a version with some extra incidental music included at the end - here's a performance of just the first suite.

there is a hindi song which is sorta long (5 mins without music, 6 with) - Breathless (not really breathless, but full song done in just 16 breaths(that is roughly 3 per minute), but almost none are easily audible) - it is a romance story - meetup - love blossom - heart break - life ruined - reunion - together forever. The lyricist is one of the best hindi/urdu lyricist, maybe among the best in the world
also there are many old classical concerts (for example - beethoven) which are music only and at times were in conjunction with plays or dramas going through stories

Swans - Bring The Sun/Toussaint L'Ouverture
It's 34 minutes but it's kind of 2 songs. It has lyrics but they're more of a vibe than actual coherent thoughts. The first half is like a slowly swelling religious fervor/extacy with a great climax. If I were ever to join a doomsday cult and we all go crazy and kill ourselves, we would do it to that song. The second half is expressing feelings of disgust during moments lost in thought while plotting revolution.

The Mystic Crystal by Ninja Sex Party is a great story song.
Also most of TWRP has songs that tell stories, like Starlight Brigade or Black Swan

This is a pretty epic story telling song by a dude called Ren.
The Tale of Jenny & Screetch and Violet

It's not long, but I really like the feel of Whole World Knows by Adia Victoria. It's about a girl with a secret drug problem (that the whole world knows about) as she spirals out of control. The symbolism is heavy, the syrongly religious family can't or doesn't help and it's a catchy tune.

Achilles, Agony and Ecstasy in Eight Parts by Manowar
Rime of the Ancient Mariner by Iron Maiden

Anything from Yorushika

Dream Theater does a really long song almost every album, but they all have words
- Stream of consciousness from train of thought and dance of eternity from meteropolis pt. 2 are really good, long-ish instrumentals that kind of tell a story.
  And to answer OP: Metropolis pt.2 by dream theater is a great concept album that has an interesting story to follow.
- Images and Words, for that matter.

Halloween by Helloween.
2112 by Rush.

For comedy, Better Midler's Otto Titsling tells an urban legend about how the bra was invented and it's freaking hilarious, with great singing.
If you want something more powerful but emotional, Linkin Park's album, 1000 Suns, if you listen to it, in order, tells the horror of the atomic bomb in a way that feels like your just listening to awesome rock music. Follow that up with the song Mike Shinoda; the rapper/musican/writer from Linkin Park; made called Kenji and it paints a dark story about how his own family was locked inside US concentration camps, during WWII, just because they were Japanese. Family/Friends died in that camp... and those that got out found their houses destroyed and graffitied by racists. It's really powerful and shows a side of the band that most people don't know.

Exquisite Corpse is ostensibly a George Watsky song but the featured artist list includes Adam Vida, Chinaka Hodge, Grieves, Wax, Rafael Casal, Daveed Diggs and Dumbfoundead
It's called what it is for a reason, and it's also a 10-minute long epic poem about the post-apocalypse. One of my very favorites.
It's all words though.

Olias of Sunhillow alternates between instrumental and lyrical tracks, and both tell the story of a bucolic species going to space in a wooden boat. It is the proggest of prog rock. If you enjoy anything by Yes, this is the main lead guy's solo debut, and it is right in the same notch as Fragile and Close To The Edge.