All is lost if one abandons Hope. 
I wasn’t exactly original material but… Jesus Christ Superstar.
Just about everything from the Alan Parsons Project
Savatage: *Dead Winter Dead *and Wake of Magellan
I hadn’t heard of this band and decided check them out on Youtube, and holy crap, I’m glad I did. Thanks for giving me some new music I need to listen to!
I give you the utterly bizarre and wonderful Colonel Jeffery Pumpernickel - A Concept Album. It’s literally too strange to even attempt to describe, you love it or hate it. There are references to childhood hallucinations, underwater fire battles, and hookers mistaken for wives long gone. I’m in the love it camp.
Or how about some epic Middle Earth, Simarillion style, from German thrash metal band Blind Guardian?
How about the most obscure concept album by a group that’s in the Rock and Roll Hall of Fame? I doubt anyone even remembers they did one (no one’s mentioned it yet), but it’s actually quite good.
It’s The Genuine Imitation Life Gazette.
By the Four Seasons.
It flopped because Four Seasons fans weren’t interested in an ambitious concept album, while those who would have been interested a concept album would never have listened to the Four Seasons.
Captain Lockheed and the Starfighters
and
by the immensely underrated and immensely talented Robert Calvert
“Captain Lockheed” and “Lucky Leif” have Brian Eno, Arthur Brown, Lemmy, and members of Hawkwind guesting on it. Sort of a “who’s who” of '70s British psychedelia. And “Lucky Leif” in fact was produced by Eno.
“Hype” has an accompanying novel, which I would dearly love to get my hands on.
I’m just going to stick with The Wall and Tommy. Why Led Zeppelin never wrote or ripped off a concept album idea is beyond me. it would have been epic.
Seconded on both of those.
I’ll also add Gentle Giant’s Three Friends.
I do have one small issue with the original list, though, and that is the inclusion of Holst’s The Planets. It wasn’t written as an album, and it really con’t be considered a concept album any more than a recording of Beethoven’s Ninth Symphony can.
Electric Light Orchestra’s Time is a rather interesting science fiction concept album.
It chronicles the experiences of a man taken from his time in the 1980s and displaced into the world of 2095. Some consider this to be the last great ELO album.
Oh, please. That album is fantastic, got rock music onto Broadway, has been translated into almost every language there is, and has never gone out of print.
It’s good to see the first ones that came to mind already on the list (Thick as a Brick, Metropolis Part 2, Brave, Fear of a Blank Planet).
It’s fun to see so many outside the progressive genre, given the association between the two.
Let me throw out an obscure one. First is Kadath Decoded by Payne’s Gray. I bought this in college without ever hearing a note based on a raving review, and I was rewarded. It’s based on Dream Quest for Unknown Kadath by H.P. Lovecraft. Many songs are now available on You Tube, but I don’t think you can get it in print.
I’ll throw out an 80s masterpiece: This is the Sea by The Waterboys.
Voivod – Dimension Hatross, and Nothingface are both masterpieces, IMO, although Nothingface was much more critically acclaimed. Science fiction storytelling from progressive/metal French-Canadians.
Sepultura – Dante XXI. Brazilian thrash metal band’s opus based on The Divine Comedy.
This is going to be, hands down, one of the best.
Did you know that the psychiatrist isn’t innocent in the mix? He is the incarnation of the scorned brother, and he hypnotizes the protagonist in the end to crash his car, thereby completing the cycle once again.
Nine Inch Nails - Year Zero
Besides anything by Pink Floyd, my favorite themed album is The Black Parade by My Chemical Romance. Doesn’t tell a single story per se, but rather songs sung by characters who are dying or just have died. Besides Teenagers which was tacked on at the end and doesn’t really fit the theme well. Unless you fanwank that the singer was gunned down by a crazed teenager, which has almost no support from the lyrics.
Wilco - Yankee Hotel Foxtrot
Eagles -* Desperado*
Electric Light Orchestra - Eldorado
Nobody has mentioned Machina: The Machines of God by The Smashing Pumpkins. It has more of a story than Mellon Collie, but then again MCIS’s concept is broader and looser. In any case, Machina is a gorgeous emotional rollercoaster, and I have championed it since it arrived in 2000.
Well, Bob Gaudio was a very talented songwriter who could SEE where the music business was going, and wanted to move with the times… but as you observe, kids who’d once loved “Rag Doll” and “Walk Like a Man” were never going to like a concept album, and hippies already regarded the 4 Seasons as hopelessly uncool.
To SOME extent, the Beach Boys had the same problem.