My Life In The Bush of Ghosts by David Byrne and Brian Eno.

The band[s] that jumps out at me when I think unique/original is anything that Les Claypool touches. It's never just him but he has a knack for finding people with unusual talent to make something different. Even when they are doing covers. For example the Frog Brigade doing Pink Floyd's Animals.

Tom Waits*

The Pixies*

Portishead*

Kruder & Dorfmeister the K&D Sessions

Massive Attack*

But maybe the most uniquely gifted musician on my list would be Richard David James.

Godspeed You! Black Emperor - F♯ A♯ ∞

Jean-Michel Jarre - Concert in China

The Prodigy - The Fat of The Land

It's a one of a kind album. I don't think the prodigy ever made another album that good. And I don't think there is anything else out there similar to it. It has its own energy, it's definitely a unicorn type.

Prince - Sign O the Times

One of the few albums I listen to beginning to end.

Also, Pink Floyd. Pretty much any album, but specifically Dark Side of the Moon or Wish You Were Here.

Future Shock by Herbie Hancock. Dude released like 25 jazz and funk albums over two decades, then in '83 just drops a hip hop bomb

Rockit

Also, Dr. John - The Night Tripper. 60s psychedelic New Orleans perfection

Cake's first album Fashion Nugget is the kind of unique that we rarely see twice.

I'll throw my few in here:

Lemon Jelly - KY
Paul Simon - Graceland
Air - Moon Safari
Portishead - Dummy
Alt-J - An awesome wave

Here is mine.

https://youtu.be/J2WP-55FLNk

Such a unique time when it came out. Electronic music was at peak experimental stage in the late 90’s. Kind of like B**ches Brew was the peak 60’s psychedelic experiment. This album was the perfect culmination of two masters of world music, psychedelic trance, and ambient music. Simon Posford is the absolute genius sound engineer at the peak of his game and Raja Ram was the old hippie wizard guiding him through realms unknown.

The two i listened to most when i was young were Sgt Pepper and Dark Side of the Moon. Happy for the vinyl revival so my kids can experience the two sides of an album.

The Postal Service

There are many synth artists that try to target a similar feel, but the way they tug on your emotions with just the subtlest of sounds. Everything feels like it’s meant to fit. Never has a song made me feel more homesick than Recycled Air. And I don’t even want to go back home.

Honorable mention goes to Moon Safari by Air. First time I heard every song on that album felt like I’d heard it before in a memory.

Porcupine Tree - In Absentia

I wanted to add some of my faves!

• Floating Points, Pharoah Sanders & The London Symphony Orchestra

• William Onyeabor - Who is William Onyeabor? - An enigmatic and reclusive Nigerian funk jazz wildman who was prolific and fairly popular in Nigeria in the 1970s. Let's Fall in Love is so innovative!

• Miles Okazaki - The Sky Below - Just brilliantly innovative avante-garde jazz and guitar. I was struck when I first heard this album

• Smoke - Everything - A group of friends and musicians quietly got together in the heart of San Francisco to record this mysterious, challenging and psychedelic jazz trip. The whole album is a journey and should be heard at once, but if you just want a taste try this timestamp

• The Flying Luttenbachers - Destroy All Music - The song Fist Through Glass is the song that got me into jazz! I heard it on a late night radio show called Brave New Waves while coming down from mushrooms lol

Endtroducing by DJ Shadow

It's his inaugural album and there's never been anything quite like it. Even his follow up albums, with his unique sound, feel a bit different than this one (not in a bad way, but I don't think they meet your unicorn criteria).

Also, I think this easily goes in my top ten albums list.

Pet Sounds by The Beach Boys

The Refused - The Shape of Punk to Come ... blending melodic, hardcore, jazz, and electronic into one punk album

Salmon - Paco Drop the Chicken ... Very eclectic rap / punk, beat-oriented with lots of changes. A personal favorite "local" band.

2112 by Rush

In-A-Gadda-Da-Vida by Iron Butterfly

I'm the only person I know that's heard side 2

Captain Beefheart

The Tiny

Future sound of london

Ren

Ween - Chocolate and Cheese

Also Nightmares on Wax - Smoker's Delight, for absolutely capturing a certain mood

Radiohead—Amnesiac (especially the B-sides) Mr. Bungle—California ミラクルミュージカル—Hawaii: Part II (strongly related to Tally Hall, which is famous for their hit debut Marvin’s Marvelous Mechanical Museum) Brian Wilson Presents SMiLE (my preferred recording of this legendary unfinished album for its complete orchestration, but I very much get the argument that it just doesn’t sound right without the Beach Boys’ voices, so I also recommend giving the Dae Lime mix a try for its combination of original and deepfaked vocals)

I'm loving these comments, so many great albums! And a ton I've never hear of and will need to check out.

I have a few of these, but two that really jump out at me are

• The Inevitable Rise And Liberation Of Niggy Tardust - Saul Williams
• Music to Make Love to Your Old Lady By - Lovage
• Common People - William Shatner

These are albums that you've just gotta let play.

e: can't believe I forgot Shatner!

I really like Pretty. Odd. by Panic! At the Disco - it sort of reminds me of the later Beatles albums but is still unique.

A Grand Don’t Come For Free by The Streets. I love this album start to finish and it’s got a great story right through it.

First time I heard it I’d gotten an email from Vice promoting it and I clicked the link thinking it would just be the first 20 seconds of each song but it was the whole album! Was just starting a movie but I never watched it, just listened to the album straight through. So good.

Avalanches, Since I Left You

The shaggs.

A fortune teller told a father his kids were destined for stardom. Empowered by this, he forced the teen/adult kids to form a band. The result breaks all the rules of music. ALL of them. Ones that you don't even know existed. Frank Zappa considers them better than the beatles

The first, like, 5 albums by They Might Be Giants are unique in their own ways. Just different blends of wackiness and musical sophistication, it's sublime.

I'll nominate Deep Forest's 1992 self-titled album.

• CocoRosie - Grey Oceans
• Cornelius - Point
• Opeth - Pale Communion

Ugly Casanova. Someone left modest mouse on the burner for too long and made a powdered concentrate.

Literally every album by The Mars Volta. Each one is unique and I'll never find anything like them again.

Yanni-live at the Acropolis. There's was a brief moment in 1994 when yanni actually achieved world peace. Also Tribute, another live album, that shows how unbelievably massive yanni was. He sold out a show at the fucking Taj Majal.

Anna ash and the family tree- hello friend, from bird above. An indie folk album that's a perfect cross between a prairie home companion and the hipster folk Renaissance of the early 2000s.

Pity sex-dark world. One of the best albums out there. Emo shoegaze garagy jams with killer guitar work.

KLF - the White Room . It is a quite unique combination of a early 90s dance album (with a few bangers that still sound good) and road movie soundtrack.

Also, excellent tread!

Igorrr - Spirituality and Distortion.

https://en.wikipedia.org/wiki/Spirituality_and_Distortion

King Gizzard & the Lizard Wizard - Flying Microtonal Banana

Lemon Jelly - lemonjelly ky

The Flashbulb - Opus At The End Of Everything

I'm gonna resist quibbling about what "completely unique" ought to mean, but in the spirit of how people are answering, I'll submit Daliborovo Granje, Hainin. https://daliborovogranje.bandcamp.com/album/hainin

Croatian psychedelic instrumental rock.

Ha, I came here to say Bitches Brew before seeing it was in the OP!

I'd add Loveless by My Bloody Valentine: much-imitated, but there's nothing quite like it.

Also, my early '90s bias is showing here, but In Utero by Nirvana is uniquely brilliant. No one's melded beauty and ugliness so successfully in any medium.

Any album by Pink Floyd.

Even mostly works if you compare said album to other albums by Pink Floyd. Dark Side of the Moon as a classic notable callout.

My Bloody Valentine - Loveless
Nothing sounds quite like it

Cocteau Twins: Heaven Or Las Vegas

I've been trying to find something similar to Holly Herndon's Proto, but haven't succeeded yet.

https://www.youtube.com/playlist?list=PLWGJxgOf-Z3CW7tJoN9f4lzIf8CEuMgne

Loving and saving this whole thread, I'll add in

Ones & Zeros, Vol. 1 - 3rdegree, not SUPER unique, but it's instrumental and commitment to they're concept album's theme of uploading your consciousness into the internet gives it a ton of charm!

Larks' Tongues In Aspic - King Crimson , very surprised I haven't seen this one in the thread, a classic weird ass prog album by the Kings of Prog themselves (IMO of course). They got a guy to do a bunch of random sounds for the album and he left to become a monk days before they started the album tour lol.

Aphex Twin and Boards of Canada.

Neil Young, Le Noise is amazing on a good system. The sub sub octave acoustic efffect is very unique.

Protomen volume I - they purposely went against arbitrary recording "laws"

Rush-2112, moving pictures

Also a rare one: Burlap to Cashmere, ,is there anybody out there. Its soooo clearly mixed. Hard to find any in depth info on this album.

possibly Speak for Yourself by Imogen Heap but I'm not sure

Gustav holst - the planets

Makaveili - the don killuminati the 7 day theory

Madlib - beat konducta vol 5-6 in india

Scientist - rids the world of the evil curse of the vampires .

There are many more artists that come to mind with unique sounds but that have more than one album with that sound.

Natural Snow Buildings - The Dance of the Moon and the Sun. It's a mix of drone, post-rock, and folk that is unlike anything I've ever heard (NSB's other albums have similarities, but this one stands out to me)

Honorable mentions:

Boris - Flood

Agalloch - Ashes against the grain

Grace Cathedral Park - In the evenings of regret