Suggest one obsure album we all should hear

Sun Ra "Nothing Is"

Willie basse (Black Sheep) “Trouble in the streets LP. 

 Good rock/hard rock album!  

Lee Michaels    "Live"

One Live Badger 

Elf by Elf all three of there albums are good.
Robert Johnson Close Personal Friend
A Texas band Baby on Lone Star Records
URSA Major is also good 

Bee Gees - Odessa  (Double Album) 1969

Concordia Viols - Crye. English Viol Music.  On Metronome METCD1020. Metronomehttps://www.allmusic.com/album/crye-mw0001242600

Heatmiser - Mic City Sons (Eliot Smith's former band)

Vulgar Boatmen - You and Your Sister (pure low-key R&R pleasure)

A Man Called E  (Eels frontman - prior to)

+1 on Bruce Cockburn: I like "High Winds, White Sky : 1971 : early, happy, trippy, folky

Obscure

Ann Richards & Stan Kenton : Two Much : 1961 : slowburn jazz vocals

Sea Level : (self titled ) 1977 : smooth and funky jazz fusion, a great lineup.

Sea Level: One the Edge : 1978 : funky and musical jazz fusion, wow!

The Beau Brummels : Bradley’s Barn : 1968: early San Fran folk Rock

Ron Elliott: The Candelstickmalker : 1969 : only sole effort of Beau Brummels member : Dark and musical

Poi Dog Pondering : Pomegranite : 1995 : sonically interesting and intense release from the Austin-based musical "family’ that featured Frank Orall

Billy Price and Otis Clay "This time for real"

Firesign Theater
"How Can You Be In Two Places at Once When You're Not Anywhere At All?"

Not really sure if this qualifies as obscure. Perhaps less known and certainly underappreciated. One of the finest voices ever.

"Greetings From LA" Tim Buckley 
Unfortunately, there is no video from this album, but I did find this gem from his album "Sefronia".

https://youtu.be/LtU-9EMSYu0

Fever Tree - from 1968

Red Steagall - Lone Star Beer and Bob Wills Music (if you can find it)
Swingle Singers - Anyone for Mozart?
Glen Campbell - The Astounding 12-String Guitar of Glen Campbell
George Jones - My Very Special Guests
Koerner, Ray, and Glover - Blues, Rags, and Hollers
Koerner, Ray, and Glover - The Return of Koerner, Ray, and Glover
Love - Love
Love - Forever Changes
The Roland Kirk Quartet - Rip, Rig, and Panic
The Incredible String Band - The Hangman’s Beautiful Daughter
Townes Van Zandt - For the Sake of the Song
John Fahey - The Dance of Death & Other Plantation Favorites
The Fugs - The Fugs First Album
The 13th Floor Elevators - The Psychedelic Sound of the 13th Floor Elevators
The Flying Burrito Brothers - The Flying Burrito Bros
The Flying Burrito Brothers - Last of the Red Hot Burritos

Bartok contrasts for clarinet, violin & piano. Stanley Drucker clarinet, Robert Mann Violin, Leonid Hambro piano.
Bartok records.
the best ever.

Great thread.
Boiling Point D2D

Not that obscure . . . but Lhasa De Sela's "The Living Road"

Mùm. Finally we are No-one

https://www.youtube.com/watch?v=9R1lYsF4W0k&list=PLplZ_yA5BHkJ3Wrr2_BDhlhy44FTkEycF

Steve Vai   - Flex-Able Leftovers Vanessa Fernandez   -  Use Me

Hedvig Mollestad Trio: Enfant Terrible

Flim &/and the BB's - Tricycle  -
Not sure if it's obscure but great music nonetheless.

https://m.youtube.com/watch?v=YCgIorbove4

Olu Dara - In the World

I have a solid list that you guys may not have heard

Oteil and Peacemakers  - Love of a lifetime or Believer

Some offshoot not well known Garcia stuff unless you are a head.  All might find them interesting
Hooterall
Fireup

Diga Rythm Band- Mickey Hart

Danny Cox- Life at the family dog or other stuff from him

Every time I come across a copy of Ralph Graham's album Differently in a used record store (which is often) I buy it and give it away to a friend. Great early-70s soul, halfway between Bill Withers and Johnnie Taylor. 

It was finally uploaded to the major streaming platforms, but it sounds like a crappy needle drop from a noisy old copy. 

Very obscure, but a lot of fun for fans of a certain Brazilian style flair, although it's French. 
Henri Texier - Amir and Varech

Not a very good recording, but can be entertaining...
Rick Wakeman, Journey to the Center of the Earth.

Igor Stravinsky
L'Histoire du Soldat

Deutsche Grammophon
recorded 1975
Boston Symphony Players

This never made it to CD.  It's an extraordinary performance, both musically and how well it was engineered.  Just marvelous.  

"Loop-Finding-Jazz-Records" by Jan Jelinek (2001). This minimalist electronic ambient album is quite special. Great for late night listening.

It might be difficult to find a hard copy, but you can check it out at youtube:

https://www.youtube.com/playlist?list=OLAK5uy_mRqd3w68qYN4deTCJUEdJdyMiXwBSBaw4

While none of these are sonic spectaculars, I’ve always enjoyed listening to:
1) "Living with the Animals" by Mother Earth (lead singer = Tracey Nelson and song writer Powell St. John who also was with the 13th Floor Elevators)
2) "The Psychedelic Sounds of the 13th Floor Elevators" (arguably, the first psychedelic rock band and certainly one of the most interesting)
3) "On the Shore" by Trees (a short-lived psychedelic folk-rock band somewhat reminiscent of Fairport Convention)4) "Mirror Man" by Captain Beefhart and the Magic Band (the Captain at his best)5) "The Loading Zone" by The Loading Zone (a much maligned "second rate" house band for the Fillmore and a very harsh recording on RCA records but it’s on Tidal and it brings back a lot of memories)
6) "Ahead Rings Out" by Blodwyn Pig (evocative of early Jethro Tull, not surprisingly given that at least one member of the group played in the other band).
7) "The Sons of Champlin" by The Sons of Champlin (sort of like Tower of Power, again there were personnel exchanges between these groups)8) "Big Brother and the Holding Company" (with Janis as the lead singer, doing the finest renditions of "Ball and Chain" and "Summertime" I’ve heard)9) "My Griffin is Gone" (by country rock singer Hoyt Axton but it’s not country)
10) "Buenos Noches from a Lonely Room" (Dwight Yoakam in an interesting performance and an excellent recording but in my much disliked country music genre, likely an artifact of me growing up in Phoenix and having to listen to that on the radio)11) "It’s a Beautiful Day" by the group of the same name (the San Francisco sound at it’s pinnacle).

Days of the New--Yellow

Masked Marauders

Cardinal Trait - You Already Know

Lowell George- Thanks, I'll Eat It Here

The Restoned - Stories of the Astral Lizard

dweller2  I was going to suggest Wishbone Ash's Argus for the way-cool and melodic dueling guitars, but you beat me to it, so here goes:  Frank Zappa's first CD was a double, Apostrophe and Overnight Sensation.  He absolutely had his best musicians during this era.  The instrumental title track to the former was written for the ex-Cream bassist Jack Bruce, and he romps.  Jean-Luc Ponty appears on violin, and George Duke asks the question, "Why Does It Hurt When I Pee?" , with references to "The toilet seat", and certain anatomical parts feeling like a "Pair of maracas".  Zappa's guitar work also superb, as are his compositions, and we learn about "The Slime oozing out of your TEEVEE set".

Buddy Guy's Living Proof.  Serious blues from the man whom Eric Clapton called the best guitar player in the world, and about whom Jimi Hendrix said that Heaven would be lying at Buddy Guy's feet while he performed.  In addition to the great electric guitar blues, there are acoustic songs that should be in all stereo demo rooms, in order to test speakers.  

Fleet Foxes self-titled Fleet Foxes

and a desert island fave for me that is obscure to many 
  - Dave Grisman Quintet 80

'Episode' by Avo Demirdjian, electric violin+band

Here is some prog rock from 2016. Start with the 3rd track, when the album really starts to take off. Here's that track at YouTube -- as good as it is here, it truly shines in hi-rez.
Trust me on that. I mastered the album.
https://www.youtube.com/watch?v=dAgP-Su0bJo

Knopfler -  Good On You Son

Mainstream, but awesome. 
Great textures and groove throughout song and actually the whole album. 

https://youtu.be/JIBCHh-fMUE

Donovan - A gift from a flower to a garden. One side electric and the other side acoustic. The acoustic side beautifully ethereal.

Tom Robinson Band,  "Power in the Darkness"   1960's Brit Rock that still sounds good.

Olu Dara,  "In the World" a surprise pick by Stereophile  Magazine as the album of the month some twenty years ago.

While obscure is highly subjective, I love this post!  So I will post more than one suggestion!

My top two "out there" pics are in the new age-ish category (though new age does these recordings a disservice):

1. Deux Filles - Silence & Wisdom
2. Popol Vuh - Aguirre

If you are into the ECM jazz label, which could be obscure for some but hardly so for others, there is one release that is an absolute gem without much attention:

1. David Darling - Cello

I always loved these two 80s releases which never got too much attention (though some may disagree) ... these are in the 4AD / Dead Can Dance genre:

1. This Mortal Coil - Sixteen Days/Gathering Dust EP
2. Colourbox - Best of Colourbox 82/87

For a last song recommendation, something from a well know band:

1. The Clash - Bankrobber/Robber Dub from Black Market Clash

Michael Chapman - Life on the Ceiling and since nobody sticks to one album, Mother Goose - Stuffed

Bob Seger - Smokin’ OP’s

Van Morrison - Live at the Lions Share 1971

A lot of people seem to be struggling with the definition of "obscure."

I've been listening to a lot of Blues and Prog Rock lately, so my high recommended Prog albums (that you won't hear much about here in the States) are by Southern Empire, Riverside, Porcupine Tree (Steven Wilson), Moonrise.
Then there are some blue artists in the States that you won't hear much about but are worth hearing like Shuggie Otis (Strawberry Letter 23), Billy Paul, George Benson.
There's is a lot of old vinyl music out there that deserved to be heard and those albums you may not find in the new vinyl box and this is what makes them obscure. ChuckStereo

Triumvirat's "Illusions On a Double Dimple," especially for the acoustic guitar and electric bass in "Lucky Girl."

Bettie Serveert 'Palomine'

+1 for Triumverat! Also "Sparticus" not too shabby either.