Symphony X - Love them. All of them are great musicians and they write some great material
Ayreon - I only have the 2 Universal Migrator albums. The second one is awesome, the first one, not so much, IMO. The Star One DVD, "Live on Earth" is a mandatory buy, though.
Dream Theater - Absolutely love them, in spite of what it may seem when I comment on their recent material.
Angra - Greatest power metal band out there, period. And not just because they are fellow Brazilians.
Yngwie Malmsteen - Hmmmm, Ingvai can play. His first 2 records are also mandatory if you are into neoclassical stuff. After that, he seems to have fallen into a rut and just rehashes his old material. It's a shame, really, because there's no denying he's an amazing talent.
Sonata Arctica - Another band I'm really fond of, though they are more of what I call Scandinavian power metal.
The Stratovarius influence is pretty obvious in their music, but they have taken it a step further, IMO. Their singer has a better voice and their music is not as repetitive as Strato's (even though you can only take that style so far).
Rhapsody - I love my cheese (that much will become clear with time
, but Rhapsody is where it gets too much. The music isn't all that bad really and they're all great musicians, but the final result just grates a bit too much with me.
Iced Earth - not prog at all. I don't know where people fit them, but to me they are more thrash metal than anything. I used to be a bigger fan of theirs (their triple-live cd "Alive in Athens" slays), but "Horror Show" and the soon-to-be-released "The Glorious Burden" seem to lack something, writing-wise.
Hammerfall - Bleh. Can't stand their stuff.
As for other prog bands, I'd definitely recommend 2: Savatage and Pain of Salvation. I can't say enough good things about Savatage, but they only become really proggy from "Handful of Rain" on, when they start using counterpoint vocals and stuff like that. Until that record, they were more straight ahead metal, can't really pinpoint how they would be labeled.
Pain of Salvation is a great Swedish band. Tough to describe what they sound like, seeing as I'm yet to hear anything similar to them, but I guess you could say there is a definite Mr. Bungle influence with a proggier twist to it.