Funnily enough I wrote a blog about this relatively recently, although I covered concept albums to some extent which is beyond the scope of this thread.
I think when it comes to albums you can't listen to the whole way through it's best to stick to those by artists you like or at least tolerate - I could think of many albums I couldn't listen to the whole way through by bands or singers I dislike.
Some albums I really like listening to through*:
Blood on the Tracks (Bob Dylan) - Consistently great songwriting throughout but also manages to balance the highly emotional songs (Idiot Wind, If You See Her Say Hello) with the elaborate storytelling of Lily, Rosemary & The Jack Of Hearts and the bluesy Meet Me In The Morning.
Love Over Gold (Dire Straits) - I find this a pleasure to listen to this from start to finish, it has their best song - Telegraph Road - but the other four are also very strong, with some great arrangements (the power chords on Private Investigations!) and excellent writing (the clever and funny Industrial Disease).
On The Border (Eagles) - Has a nice range of different musical styles with rock songs like Already Gone and James Dean and some country songs My Man and The Best Of My Love, and a consistently excellent set of songs.
Rumours (Fleetwood Mac) - It's difficult to beat as a collection of individual songs but put them together and they are even better, especially if you're aware of the breakups between the band members at the time.
Houses of the Holy (Led Zeppelin) - Every track is almost completely different, with much of it covering new ground for the band (reggae on D'yer Mak'er, prog on No Quarter etc.) and it's all good, most of it is more than good in fact.
Meddle (Pink Floyd) - Great album, and unlike its successors it's not a concept album, the fact that Echoes makes up half the album helps but add the first three songs and you've got an album which is brilliant for the vast majority of its running time. I like San Tropez and don't mind Seamus, which I suspect might prevent some from listening to this album through.
After The Gold Rush (Neil Young) - Another collection of songs that work brilliantly together, has great songs but it's more than the sum of its parts. Also manages to fit Southern Man in amongst largely acoustic compositions.
Rust Never Sleeps (Neil Young & Crazy Horse) - With great acoustic and electric sides, this of Neil Young at the top of his game at both and starting with My My, Hey Hey (Out of the Blue) and closing with Hey Hey, My My (Into The Black) was a great idea.
*There are others I enjoy listening to through, I'm someone who likes to listen to whole albums, but from the non-conceptual albums these ones stood out.
Albums I don't like listening to through:
X&Y (Coldplay) - Not down to any one track - although I've never been too keen on Twisted Logic - but it's too long and a bit too samey with a couple of exceptions and with so many anthems it gets exhausting to listen to. One half of this at a time is enough I find.
Brothers In Arms (Dire Straits) - I'm rarely in the mood to listen to the tracks on side one and those on (the IMO superior) side two at the same time, and I sometimes lose interest during Your Latest Trick and Why Worry?.
Tusk (Fleetwood Mac) - Side 3 has three weak songs in quick succession - That's Enough For Me, Brown Eyes and Never Make Me Cry (the worst of the three, which I find very boring and hardly ever play), I can listen to the rest of the album, which is generally very good, just fine but I find that section to be a bit of a road block.
A Momentary Lapse Of Reason (Pink Floyd) - I find Dogs Of War to be awful, I don't like the music, vocals or lyrics (I don't have a problem with Pink Floyd minus Waters, but I consider this to be a bad pastiche of Roger's songwriting). I'm not a big fan of the rest of the album but it's decent enough by the standards of most.
The Joshua Tree (U2) - This is the best album I've put in this section, I certainly prefer to the others I've included but I really have to be in a certain mood to get through Bullet The Blue Sky (don't like the spoken word section), which more often than not I skip. It's odd because I really like everything else on here.