Your favorite 'concept' album

King diamond Abagail, the eye, abagail II, the puppet master, 
The graveyard, Them,  many cross lines with each other.
the man is a genius!

Iron Maiden 7th son
queensryche operation mind rime
iced earth. Night of the storm rider!

 There’s more, but that’s all that comes to mind now.

Titus Andronicus - "The Monitor"

Great concept album. My 17 year old son turned me onto it. Man, that kid's got great taste in music......

My definition of a concept album is not just one in which a particular theme or concept is explored but also one the I get lost in and that I would prefer to listen to as a whole. I also feel that this should be the intent of the artist. Lots of albums "work" as a cohesive collection of songs (Aja - Steely Dan) but don't fit my idea of a concept album. I look for almost a symphonic structure.

Just my take on it and some of the ones I list might not even fit my own definition.

A few that I don't think have been mentioned:

Astral Weeks - Van Morrison. My favorite concept album and one of my favorite of all albums.
Vedon Fleece -Van Morrison. Not as "conceptual" as Astral Weeks and not as good....but still good.

Morning Phase - Beck. To me, a true concept album that even has recurring themes throughout like a symphony.
Sea Change - Beck. Not as mature or cohesive as Morning Phase.

Khruangbin- Con Todo El Mundo. Superb and NEW! Not many solid concept albums coming out these days.

Lay It Down - Cowboy Junkies. Maybe?

White City - Pete Townshend


Agree with some already mentioned:

Soul Cages - Sting. Very thematically cohesive. Well recorded too.

Wish You Were Here- Pink Floyd. A concept album by every definition of the word as is everything from DSOTM onward but I think WYWH is their best and most cohesive as a concept album. Animals I'd place second. Not saying those are their best albums, just best in terms of the "concept" idea. The Wall is epic and I love it....but maybe a bit too epic. It can be a little tiresome in a Wagnerian way.

Rush is tough. I love Rush. Most of their albums up through Suburbs (I never liked their later stuff) are strongly conceptual and thematic but I don't know of any of their albums that carry the concept/theme through the whole album. If I had to pick one I'd say Hemispheres.

+1 for Operation Mindcrime. I need to give that another listen. It has been a while. 
Captain Fantastic is my favorite Elton/Taupin album 
  
2112 also, but Quadrophenia is my favorite.

Neal Diamond "Tap Root Manuscript" side 2, way before Paul Simon's "Graceland".