The most musically complex prog band(s)?

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!

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.      

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.

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.

Univers Zero and Henry Cow.

Depends, for me complex is Flairck and in the same time Gentle Giant and Symphony X. Each one in his own way. How can you describe complex??? Progressive music in general is complex, at least must be this way.

Coming back to this topic, I think I forgot Protest the Hero...hella hard, I try.

Tapfret wrote: For Zeuhl I would have to go with (I know some Magma zealot is going to shoot me) KoenjiHyakkei.

From what I've heard, I think you're right!

Paulieg wrote: Classic Prog:  Gentle Giant, King Crimson, Mahavishnu Orchestra, Banco Del Mutuo Soccorso, ELP, etc... tons of good old stuff. Modern Prog:  Dream Theater, Fates Warning, Spiral Architect, Zero Hour, Planet X, Rush, Symphony X, pretty much all prog metal bands.

Rush is NOT metal!!! Anyone who says that should die.

TFTO = Tales From Topographic Oceans