Albums that you listen to straight through / start to finish whenever you put them on!

The OP makes a couple of really good points:

1) Albums that you truly want to listen to all the way thru are rare.

2)But,  it's a good idea to listen to the entire album because our tastes change over time. I know that I've rediscovered countless songs that I either forgot about or just didn't appreciate initially. However, I know I'll never change my mind about "Alabama Song" from the debut album by The Doors.

JJ Cale - "Naturally"
Bruce Cockburn - "Inner City Front"
Lloyd Cole & Commotions: "Rattlesnakes"
Crack The Sky - "Crack The Sky"
Michael Franks - "The Art of Tea"
Love - "Forever Changes"
Pousette - Dart Band - "Pousette - Dart Band"
Wishbone Ash - "Argus"

Blue Oyster Cult - "Tyranny and Mutation"
Maria McKee - "Peddling Dreams"
Iris Dement - "Sing the Delta"
Crowded House - "Temple of Low Men"
The Band - "Music from Big Pink"

And one very important pair not to be missed and always played through (NOTE: Not necessarily vinyl, but albums none the less).

Tom Waits - "Mule Variations" 
Tom Waits - "Alice"

Fascinating... I guess I am a rare bird. But, of course, the bird is the word.

I listen to both sides of a record only the very first time and rarely afterwords. I get a sense of the vibe of the side and play one or the other depending on mood (and guests) forever afterword. When a side ends I assess the mood and, generally speaking, I am so inspired by that music I want to explore another record to push that envelope or completely change tack. Sometimes the mood does lead to flipping sides. Sometimes. I did that yesterday once.

Digital is a whole other story but does still includes listening to the full album the very first time. In fact, I now wish Roon had an option to display and play as album sides.

Here is a copy and paste of some of the responses (not all)
so excuse me if I missed a few.
Interesting and diverse selection of albums thanks everyone.
If you’re late to the party on this feel free to jump on in. 
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The Moody Blues - The Days of Future Passed
Pink Floyd - Dark Side of the Moon
Alan Parsons Project- I Robot
Miles Davis - In a Silent Way
Weather Report - Black Market Paul Simon - Graceland 25th anniversary reissue
The Beatles.... Abby Road
Eagles.... Hotel California
The Cars.... The Cars
AC/DC..... Back in Black
Pink Floyd.... The Wall
Chuck Mangione…. Feels so Good
Henry Gross - Plug Me Into Something
Led Zeppelin - l
Tom Petty All Albums
Derek and the Dominos
The Beatles All Albums
The Rolling Stones - Beggars Banquet and Let It Bleed and Sticking Fingers, Some Girls
Jethro Tull - Aqualung
Jimi Hendrix - Smash Hits
Brian Protheroe-first 3 Chrysalis albums
John McLaughlin-Electric Dreams, Adventures in Radioland, Tokyo Live
Richie Cole-Bossa Nova Eyes
Joni-Court And Spark
ELP-Tarkus
The Bearles-A Huge Melody (or my covers version)
The Beatles - Abbey Road
Pink Floyd - Dark Side of the Moon
The Who - Who’s Next
Elton John - Goodbye Yellow Brick Road
Fleetwood Mac - Rumours
Supertramp - Breakfast in America
Steely Dan - Can’t Buy a Thrill
Led Zeppelin - Houses of the Holy
Bruce Springsteen - Born to Run
Stevie Wonder - Innervisions
Boston - 1st Album
Bob Dylan - Hard Rain
Bob Dylan - Street Legal
Aldous Harding - Designer
Van Morrison - Wavelength
Dire Straits - Communique
Dire Straits - Dire Straits
Chris Whitley - Living with the Law
Willie DeVille - Sportin’ Life
John Coltrane - "A Love Supreme"
Ray Charles - "What’d I Say"
Diana Krall - "Love Scenes"
Paul Desmond - "Feeling Blue"
Tom Waits - "The Heart of Saturday Night"
Gerry Mulligan - "Night Lights"
Quincy Jones - "Body Heat"
De La Soul - "And The Anonymous Nobody"
Enya -Watermark
Patricia Barber- Cafe Blue
Hope Sandovar- Most Any
Simon and Garfunkel-Sounds of silence.
War - All Day Music
War - The World is a Ghetto
Sade - Diamond Life
Sade - Promise
Gregory Porter - any album
Pink Floyd : Wish you were here, Animals
Jethro Tull: Aqualung
Supertramp : Crime of the Century, Even in the Quietest Moments
Springsteen : Greetings from Asbury Park
Steely Dan-"Aja"
Joni Mitchell-"Court and Spark"
Bob Dylan-"Blood On The Tracks"
Beatles-"Rubber Soul"
Jethro Tull-"Thick as a Brick"
Paul Simon-"Hearts and Bones"
REM-"Greatest Hits"
David Bowie-"Ziggy Stardust"
Rolling Stones-"Through the Past, Darkly"
Cat Stevens-"Tea for the Tillerman"
JJ Cale - "Naturally"
Bruce Cockburn - "Inner City Front"
Lloyd Cole & Commotions: "Rattlesnakes"
Crack The Sky - "Crack The Sky"
Michael Franks - "The Art of Tea"
Love - "Forever Changes"
Pousette - Dart Band - "Pousette - Dart Band"
Wishbone Ash - "Argus"
Mary Travers - Mary
Paul Simon - Graceland
Tom Waits - "Mule Variations"
Tom Waits - "Alice"
Blue Oyster Cult - "Tyranny and Mutation"
Maria McKee - "Peddling Dreams"
Iris Dement - "Sing the Delta"
Crowded House - "Temple of Low Men"
The Band - "Music from Big Pink"