The most musically complex prog band(s)?

DT has complex moments, but for the most part they have become very formulaic.  When speaking in prog- metal terms, there are several bands that are far more complex. Unexpect uses multiple vocalists, keys and RIO textures. In fact, I would call it "Metal in Oposition". Martyr, especially their last album, Feeding the Abscess, makes DT sound like Journey. Chile's Coprofago was extremely complex with Unorthodox Creative Createria, throwing in Holdsworth style jazz sections. And of course, Ron Jarzombek and Spastic Ink. The cool thing about RJ's projects is he explains the meanings behind the complexity and does it w/o inflated ego or condescension.  Someone also mentioned Behold...the Arctopus, a fine choice indeed.

The RIO/Avaunt Gard sub-genre has the greatest abundance of complex bands.  For pure complexity Zappa is the most consistent. Even when a song has an overall "straight ahead" texture, you can hear underlying complexity. e.g. One Size Fits All, Roxy and Elsewhere.  Mr. Bungle, with their "flick of the switch" style changes are also pretty out there. In this sub-genre complexity is very much in the ear of the beholder. Bands like Universe Zero, Captain Beefheart, and The Flying Luttenbachers are outrageously complex, but might lean to far into the dissonant side for many listeners. Even Zappa goes to those places with some of his work, particularly his orchestral pieces like LSO I & II, Yellow Shark. 

Jazz/Fusion also has tons of complex bands like Brand X, Return to Forever. Jazz is of course founded on complexity. Even in the 1930's, Raymond Scott was doing some very complex music. (He might fit well in PA)

For Zeuhl I would have to go with (I know some Magma zealot is going to shoot me) KoenjiHyakkei.
 
Amongst other sub-genres, Giant Giant is exceptionally complex, nobody has more vocal complexity. And of course King Crimson, lots of instrumental "talkback" and flighty finger on guitar.  

I see people in this thread answering with the more "accessible" bands. Dig deeper if you like complexity. The most complex stuff is not mass produced. For pre-1990, go with bands in the Jazz/Fusion or RIO/Avant genres. Post-1990, Tech/Extreme Metal seems to the best bet if want to hear complexity.

I know that GG and DT are pretty complex, but the most complex music i've ever heard is by Behold... The Arctopus. I think they're very interesting. It seems like they just pick a tone and a number and make that their notes and time signature. After they're done with that bar, they just do it again. Their ability to memorize such strange and unconventional music astounds me. From what I've heard they're much like Spastic Ink.

Dream Theatre, particularly on Systematic Chaos, seem very complex to me - although I do not know much about them. The Beach Boys harmonies are complicated and Todd Rundgren, on Face the Music, replicated them extremely well. Al DiMeola's and Gary Boyle's (jazz-rock) guitar playing is both complex and very fast. For almost irritating complexity I would go for Gentle Giant.      

Technically speaking, Mahavishnu Orchestra by a long shot.  Just listen to Birds of Fire, they really are on fire!  Groups like Magma and King Crimson are up there too...as well as other jazz fusion groups like Return to Forever.  These groups are special because they are beyond technicality (which often turns cheesy very fast i.e. Dream Theater etc.).  Their music has soul and muscle to back up the sound!

ELP for sure, Yes can be somewhat complex,

MTZArts wrote: On a few of their albums, King Crimson screwed around with different timing until the point where it would make a theory god like Pat Martino's head spin.

preqT0THEseq7 wrote: Between the Buried and Me

King Crimson

The most complex thing is that which is the most difficult for you to get into....

I agree, cacho, that a lot of Marillion is not entirely complex however they have the 19 minute epic Grendel that has an incredible multimovement suite in the style of early Genesis. Spock's Beard perhaps is not the most complex but once again their CDs Octane and The Light are full of interchanging time signatures and multi chord changes. I agree too that Topographic Oceans has to rank as one of the most complex CDs.