Anglagard Hybris A short-lived "neo-prog" Swedish group from the early 1990's, their first (of two) disks is wonderfully rich, both sonically and musically.  There is (mercifully) little singing (their vocal skills are not even close to being equal to their instrumental abilities).  Their second album, Epilogue, is a worthwhile but weaker follow-up.  There's also a live album (Buried Alive) but I've not heard this.
Ars Nova Book of the Dead I like most of their work but if I had to pick just one of their disks, it would be this one.  Ars Nova has always struck me as where ELP might have gone after Brain Salad Surgery if they hadn't jumped on the 1980's "let's make our music stupid" bandwagon that swept the nation.
Banco del Mutuo Soccorso (later, just "Banco") Darwin
Come in un' Ultima Cena
Although I didn't discover Banco until the mid 1990's, they've been around since the late 1960's (and are still performing).  To varying degrees, I like every CD I've ever heard from them but these two are probably my favorites (Banco purists will hate me for saying this but I think I'd have to say I prefer the later 1991 remake of Darwin ).  Lonna assures me that their lead singer is absolute proof that fat men with beards can be very sexy!
Emerson, Lake and Palmer Tarkus
Trilogy
Brain Salad Surgery

Well, these guys may not have invented progressive rock but they were one of the big three (ELP/Yes/King Crimson) who sold it to the world in the early 1970's.  Tarkus (the suite of songs, not the album as a whole) is probably the first atonal rock song (as well as one of the first "concept" pieces), Trilogy may be the best engineered rock record ever (I still hold this up as the ideal of how drums, bass and keyboards should be recorded on a rock record) and Brain Salad Surgery is the disk which, if I had to pick just one ELP album, is the one I'd probably choose,  partly for the epic Karn Evil 9 suite but also for the wonderful arrangement of the old British anthem Jerusalem and the (mostly) thrilling arrangement of the Toccata from Alberto Ginastera's first Piano Concerto.

It's not on any of these albums but I feel compelled to pay a brief homage to the synth solo at the end of Lucky Man from their first album.  This introduced a startling new type of way to end a song, even more so the way it just sort of devolves into some funny noises over a few closing cymbal crashes.  For me, this ending turns this cute little folk/pop song into an inspired work of art.

Et Cetra Et Cetra  This Quebec-based Gentle Giant-inspired band made only this one album and the only way I came across it was in a thread on an email site discussing "bands which sound like Gentle Giant."  I was struck by the message about Et Cetra because the person posting told a story of seeing them on a double-bill with GG, getting backstage and finding that the members of GG were completely caught up watching Et Cetra play.  It's true…they do sound like Gentle Giant but not in a derivative way.  This is music which is very much in that vein but no carbon copy of the original.  Well worth a listen (or several) if you can find this disk (see note below).  By the way, I've discovered recently that there are at least a couple of other bands with this same name.  I don't know anything about them but check out the guys from Quebec.
Genesis Selling England by the Pound Another stalwart of British progressive rock, in my mind, they produced some brilliant work and then sold out.  This album, however, is wonderful and it's almost always the first one I reach for when I want to hear some Genesis.
Gentle Giant Octopus There are so many good albums from these guys but Octopus stands out for me.  Almost everything I say about this disk is equally true of several others (especially Interview and Free Hand): wonderfully varied instrumentation, rich vocal arrangements, atonality as an expressive idiom (rather than just trying to be different) and lots of really irregular meters which still manage to kick butt.  When I first heard them in the early 1970's (can't recall what album), I didn't care for them…I needed to develop a lot more musical sophistication before I could get just how special they were.
Happy the Man Happy the Man
Crafty Hands
Not very many people have heard of HTM and I didn't discover them until long after they'd split up but they have a prog-rock sound that really doesn't sound quite like anyone else I can think of.  Again, I like most of their work but these first two albums are probably the best.  I believe the group has actually reformed within the last year or two but I've not heard any of their new work (friends tell me that it's on par with what they were doing the first-time around...not as a tired rehashing but as in "if you liked them then, you'll like them now.")
Jasper Wrath Jasper Wrath
Anthology
JW was a band I grew up with (all the members are from my home town of Hamden, CT) and I watched them evolve from a cover-band (sort of) playing high school dances to a fairly successful band on their way off to England.  Although they always kept some rather simple pop-tunes in their repetoire, I mostly loved them for the rhythmically complex and irregular music with frequently beautiful vocal arrangements.  Unfortunately, their one LP was marred by conflicts with a producer whose vision of the band's sound was largely at odds with the band's vision.  The result is a bit of a hodgepodge with some of the tracks (Autumn, Odyssey, Portrait of My Lady Angelina and Roland of Montevere) being shortened but still representative snapshots of their live performances (most of the rest of the disk is enjoyable enough but nothing to write home about).  In the mid-1990's, drummer Jeff Cannata dug through the master tapes of the LP plus a lot of demo tapes, some later unreleased studio material and some live recordings and put out a 2-CD anthology on his own label.  That's also difficult to find but well worth it (he's included some of the weaker pop-tunes but there are also some thrilling (if not terribly well recorded) live recordings.  For what it's worth, JW was perhaps the single biggest influence on my early prog-rock compositions and Cannata's drumming was the biggest influence on my playing
Jethro Tull Benefit
Thick as a Brick
A Passion Play
Songs from the Wood
Some people take issue with whether or not Tull is progressive-rock but for my money, they not only deserve that label, they are, in fact one of the giants of the genre.  It's hard to pick just one (or even a couple) of their disks as best.  For my money, Benefit invented the Tull sound and remains one of the all-time great rock records.  Thick as a Brick and Passion Play brought them to their most compositionally complex outings (their compositional sophistication, for me, in some respects peaks on Thick As a Brick and, in other respects, on Passion Play (most specifically, the opening 5 or 6 minutes)).  I'm also listing Songs from the Wood because, when all the prog rock bands started writing  more "radio-friendly" music in the late 70's and early 80's, Tull was one of the very few that kept the music interesting, even while going for shorter numbers.
Kansas Leftoverture Not everybody thinks of Kansas as prog rock (and a lot of it probably isn't) but I love the richness and variety of ideas on this disk.  Song for America and Point of Know Return also have some great music but if I have to pick one Kansas disk, this is it .
King Crimson In the Court of the Crimson King Before King Crimson turned into the Bob Fripp Experimental Workshop, they were a brilliant band (apologies to any hard-core KC fans who will no doubt find that statement inflammatory).  Their first album remains, for me, one of the high points of progressive rock.  This is music which wonderfully balances strict complexity with free improvisation, distorted shouting with beautiful lyricism, rich mellotron-laden landscapes with frantic BeBop-inspired riffing.  It's well over 35 years since I first heard this disk and I still love it (even the cover remains one of my all-time favorite pieces of album-art)
Locanda delle Fate Forse le lucciole non si amano piu  I don't know very much about these guys.  They made this disk in 1979 and another (Homo Homine Lupus, which was good but not in the same league) 20 years later and that's all I've ever heard from them.  I first heard Forse when Homo was already being recorded but I wish I'd discovered them earlier.  This album is one of the most stunningly beautiful Italian prog-rock records I've ever heard.  If this were only a top-10 list, Forse would still be on here.
The Monkees Pisces, Aquarius, Capricorn and Jones, Ltd The Monkees?!?!?!?!? on a prog-rock list?  It's true, most of this album is mid-60's pop music but this album has some elements which would have been surprising on a Pink Floyd album of this period much less this "completely manufactured" pop group.  As far as I can tell, Daily, Nightly has the first really prominent use of  a Moog synthesizer (at least, on a mainstream record) for creating weird atmospheric noises,  Love Is Only Sleeping is the earliest use of 7/4 in a pop song,  the nominally country-and-western What Am I Doing Hanging 'Round has a very irregular (and somewhat additive) phrase structure and Star Collector is probably the first time the "place-where-the-guitar-solo-goes" was filled with a full fledged (if not very inspired) Moog solo.
National Health Complete National Health grew out of an attempt, largely driven by keyboard virtuoso Dave Stewart (most decidedly not the Dave Stewart of Eurythmics fame) to combine a number of the best prog-rock bands based around Canterbury, England into a sort of rock orchestra.  This met with limited success but the music they did record is often insanely complex (but, unlike a lot of music which passes off free-improvisation as complexity, this was a structured complexity with carefully rehearsed music built on a lot of rich counterpoint amongst the players).  Virtually all their recorded output is now available on this 2-CD set and it's complete with a lengthy booklet (mostly written by Stewart) which is both informative and acerbically amusing.  FYI, a follow-up disk called Missing Pieces contains works which were not on any of the original albums and is well-worth owning for fans.
Premiata Forneira Marconi Per un amico
Storia di una minutto
The grand-daddy of Italian progressive rock bands, these guys are still playing together after almost 4 decades!  These are their first two albums (many of the songs (with new lyrics in English) showed up on their US-released Photos of Ghosts album.  That's a great album, too, but if you've never heard of these guys, start with the Italian disks.
Renaissance Scheherazade
Song for All Seasons
These guys pretty much defined the notion of "symphonic" rock and they probably never did it better than on Scheherazade which, unlike so many band-plus-orchestra albums of the 70's, actually is a piece for rock band and orchestra rather than a simple beefing up of the sound with some string parts.  Song for All Seasons, to my mind the last "real" Renaissance record (a number of regroupings of the band continue to perform under the Renaissance moniker today).  Overall, it's probably not as strong as Scheherezade but the opening couple of cuts (Opening Out and Day of the Dreamer) are probably my two favorite Renaissance tracks.  
Starcastle Starcastle Starcastle may not have been a great band but they were very talented and had a wonderfully inviting sound.  The first three of their four albums all sounded pretty much the same (and the now more-difficult-to-find fourth sounded like a different band altogether…you're not missing much on that one).  Nonetheless, the first album did introduce a fun, clean, rich, virtuosic sound which I still enjoy, even if the recorded performances are a bit too pristine and lacking in energy.  
Yes The Yes Album
Close to the Edge
 The last (alphabetically) of the pillars of prog-rock it's again hard to pick just one disk from them.  The Yes Album probably holds up as the freshest for me.  The sheer joy of songs like Yours is no Disgrace and I've Seen All Good People still hit me with all the thrill of the first day of Spring.  Close to the Edge has, for my money, the best lineup of musicians Yes ever had.  It's also wonderful for the epic scope of the title number.  (Tales of Topographical Oceans takes the award for the most ambitious concept-album ever and I love a lot of it but there's a little too much that falls short of the mark, not the least of which is Alan White's mind-numbingly dull drum solo on side 4).
Yezda Urfa Sacred Baboon OK…I just felt compelled to put at least one disk on here that virtually no one is likely to have heard of.  It's hard to describe this music.  It's a bit  like Zappa meets Camel meets Flash and yet it's not like any of them (although the lead singer's voice does sound a lot like Colin Carter of Flash). Just go listen.

NOTE:  Some of this music is not that easy to find.  Possibly the single most comprehensive sources for imported progressive rock is Synphonic Music, run by the very knowledgeable and very helpful Greg Walker.