My favorite is The Microphones' series of three albums, It was hot, we stayed in the water, The Glow, pt. 2, and Mt. Eerie. They have some unifying themes lyrically, but sonically, they are one giant journey from beginning to end, feeding off of eachother and growing as they progress.
I have really gotten into Ziggy Stardust recently. Fantastic album.
A more recent favorite would be Drums Not Dead by Liars. Sort of out there, but a fantastic album. It is a conversation of sorts between two characters, Drum and Mt. Heart Attack.
Also, a fun album, but sort of nuts, and not all great by any means, 69 Love Songs by the Magnetic Fields is awesome, hilarious, and weird. It is, as the title suggests, a triple album of 23 songs per disc all discussing love. Haven't listened to it straight thru yet, though.
Also, pretty much every mountain goats album goes on a theme, though not always a story. Tallahassee, for example, is all songs about John Darnielle's relationship with his father in law. Doesn't sound compelling, but it is.