Seriously- while Sinatra didn’t write his own songs, as most of the usual suspects on “concept album” lists did, he made several albums in which all the songs were chosen to fit a theme, which makes them concept albums of a sort.
Check out ***In the Wee Small Hours ***or Come Fly With Me.
In order by band:
Helloween, Keeper of the Seven Keys 1 and 2.
Iron Maiden, Seventh Son of a Seventh Son
Judas Priest, Nostradamus
Savatage, Dead Winter Dead; Streets: A Rock Opera; The Wake of Magellan; Poets and Madmen
Virgin Steele, The House of Atreus Act I and II
Interestingly, like XTC’s Skylarking, that only became a concept album after the producer, Todd Rundgren, heard their demos and came up with the concept. In the case of the Tubes, he actually co-wrote a couple of songs with them to tie the concept together.
Too new to really be called the “best” yet, but one from this year (from a member of Husker Du) I really like is Grant Hart’s The Argument, based on Milton’s Paradise Lost.
I agree 2112 doesn’t count as a concept album, but I would say The Who Sell Out does, and would further argue it’s the best of their concept albums.
ETA: Rush’s latest, Clockwork Angels, definitely is a concept album, though, so I’d pick that one for them.
Titles I own that haven’t been mentioned yet, AFAIK:
The Decemberists - The Hazards of Love
Warren Zevon - Transverse City
Aimee Mann - The Forgotten Arm
Randy Newman - Good Old Boys
Poe - Haunted
The Flaming Lips - Yoshimi Battles the Pink Robots
Sufjan Stevens - Illinois
Radiohead - OK Computer (I know the band rejects the lable, but if it walks like a duck etc.)
Some lesser known concept albums that, while not everyone’s cup of tea, I think are masterpieces…
Men Without Hats - Pop Goes the World Blue Oyster Cult - Imaginos Camper Van Beethoven - New Roman Times
…and of course I came to this thread to listen to the endless debate by the dopeagentsia of what qualifies as a “concept” album. Some of these in this thread are pretty tenuous, and one could claim that every Taylor Swift album is a concept album exploring relationship breakups.
Heart’s Dog and Butterfly
The “dog” side of the album consists of louder, faster rock songs, while the “butterfly” side of the LP is all softer ballads.