MOTM

Gentle Giant is probably my favorite as well.  I would recommend 
that anyone who is unfamiliar with them to start with "Playing the 
Fool" which is probably the best live album I have ever heard.  I 
have every album they ever did and although some of the earliest 
albums are somewhat raw I love them all.
I also love Genesis, but mainly "Nursery Cryme," "Foxtrot," "Selling 
England," and "Lamb Lies."  My favorite is the live version 
of "Lamb" from the Genesis Archives Vol. 1.  The first two albums 
after Peter Gabriel left are also pretty good, but after that they 
sort of lost me, although there is still a lot of good playing in 
the later stuff.
Yes is very good as well.  I like the epic albums "Close to the 
Edge," and "Relayer" in particular.  The Keys to Ascension live 
recordings are quite good, but too obviously sweetened.  I have the 
DVD to "Keys" and quite often the sweetened audio that you're 
hearing does not match the video, especially where there are 
multiple vocal parts and no one appears to be singing!
I would also recommend the Larry Fast stuff mentioned by others.
Peter Gabriel has some unique music which I like very much as well, 
particularly the "Security" and "So" albums.  I found his latest 
album depressing.  Too many downer songs.
As for the more electronic stuff.
I like the Tomita albums.  Although some of the sounds strike me as 
odd, some of them are absolutely outstanding. (I'm speaking of the 
synthesizer voicings chosen.)
Vangelis is one of my favorites.  I would 
recommend "Spiral," "Beauberg," and "China."  I also really 
like "Heaven and Hell," although I think parts of it are hokey.
I also have an album called "White Noise" that I know absolutely 
nothing about, but I like it a lot.
In both prog rock and electronic music, I like stuff that is layered 
sonically rather then beat based.  I like lush backgrounds rather 
then in your face virtuosity.
One more recommendation:  Jordan Rudess - Feeding the Wheel.  This 
guy is one of the most outstanding keyboardists I have ever heard 
and I think he could give Wakeman a run for his money.  However, the 
stuff he does with Dream Theater does absolutely nothing for me at 
all.