Best one I can think of is Mussorgsky's Pictures at an Exhibition (either Mussorgsky's original for piano, or Ravel's orchestration, though I honestly prefer the latter), a series of musical sketches, each one based on a different work (watercolors, I think) of artist Victor Hartmann. The suite itself is a musical "walk" through the gallery, including a recurring promenade theme that represents the walk from picture to picture, instrumentally influenced by the subject matter. Just effin' brilliant.
Other oddballs that make my sun shine include Pete Townshend's White City, Lou Reed's loosely conceptual New York, Joe Jackson's Heaven and Hell (featuring a fantastic workout on moralizers called "Right"), perhaps Tom Waits's Blue Valentines.
Pet Sounds? Sgt. Pepper? I guess both could be thought of as concept albums, but only in the context of their day. Pet holds together musically more than conceptually (and, let's be frank, the lyrics are generally pretty dumb). And the Beatles open and close Pepper as a concept, but in between, it's clear that the real theme is four blokes flying by the seats of ther pants, improvising madly.
Juliet Letters is an inspired choice, though I can understand why some hate the album. I love it. Rush's 2112 comes up a lot; but I think it doesn't stand up with any real maturity, plus Hemispheres is a lot better thematically and musically. Stevie Wonder's Songs in the Key of Life is another loose (but groovin') concept work. McCartney's Band on the Run is a fine concept album and contains some of his best solo work, though the concept itself seems to have been "Let's make a concept album!"
At the top of the list I'd put Marvin Gaye's What's Going On, clearly a modern masterpiece without rival in its topicality, emotional frankness, and sheer musical brilliance, both in the writing and the performances, especially the standout bass work by Jamerson. The topicality is dated now, true; it's become an artifact of another time. But certainly not the way that, say, Surrealistic Pillow has. Nothing in it has become silly, pretentious, or self-indulgent, the way so much of that era's music has (and so many concept albums have). It is a gem that beats out everything on Green's list, hands down. (Listen particularly as the dramatic, spoken-sung "Save the Children" boils down into a nearly supernatural groove that takes off from a piano glissando into "God is Love." Possibly the best moment on the album.)