I tend to like the overblown glory of such orchestral/operatic rock as:
Rush
Styx (“Come Sail Away” is an excellent example)
REO Speedwagon
Queen
Meat Loaf
earlier Springsteen
As you can see, these are all classics which I continue to enjoy. But who is doing this kind of work now? Or is orchestral stuff all new-agy now and not rock?
He’s old stuff, too, but have you listened to non-Yes Rick Wakeman? He’s still doing the same sort of stuff. His Return to the Center of the Earth from 8 years ago is pretty reminiscent of the 25 years earlier Journey to the Center of the Earth 9which I saw in concert)
Take a look at SPV and Inside Out records. Those are the two big modern prog labels. I don’t think you’re going to find exactly what you’re looking for, but you might find something you like.
elo
Well, if you like overblown glory with orchestral intrumentation and operatic vocals (and you’re not completely turned off by metal) you should check out the symphonic power metal genre–groups like Rhapsody and Nightwish are about as overblown as it gets. Therion is another good choice for orchestral/operatic metal. Check out their Vovin album.
Otherwise, you might like symphonic rock throw-backs like (with some album recommendations):
Ayreon- Into the Electric Castle
Flower Kings- Space Revolver
Spock’s Beard- V, Snow
You might like some earlier Golden Earring. Moontan has a number of songs that you might like. However, you’d be better off trying to find the European version, you’ll know because it has six songs instead of five, and has a nude woman on the front. Other albums include Eight Miles High, which includes an eighteen minute cover song, Golden Earring, or Seven Tears. You might be able to find the Continuing Story of Radar Love which spans a number of years the easiest in the states though.
Emerson, Lake and Palmer.
Blind Guardian. I cannot say it enough. Check them out. (Nightfall on Middle Earth is a great starting point.)
Electric Light Orchestra.
Some of Peter Gabriel’s early solo stuff (“Solsbury Hill” comes to mind).
Asia (their first two albums, in particular).
Just about anything by the Alan Parsons Project (esp. “Tales of Mystery and Imagination,” “Pyramid,” “Eye in the Sky,” and “Ammonia Avenue”).
You might like Kansas.
There are several songs by Procol Harum you might like.
Renaissance
Illusion
The Intergalactic Touring Band
They look very interesting. The review seems to have all the keywords…Epic, majestic, folk-inspired metal, “not thrashy” 
Thanks for all the reommendations folks!
Most of these are old bands. Is that what you were looking for? Or what new bands would be popular with fans of old orch rock? Try these more recent bands, I’m pretty sure that fans of big, orchestral bands of yore will like them:
Spiritualized
Lupine Howl
Spacemen 3
Happy Rhodes (person, not band)
Mercury Rev
The Flaming Lips
Jeff Buckley
Radiohead
. . . there are more that will occur to me . . .
I came in to recommend Nightwish – I’m not into metal at all, but I love their epic, fantasy-inspired sound and female vocals.
Dream Theater is another good choice. They’re heavier than most of your choices, but I’d compare them to Rush as being top-notch musicians and masters of their instruments. Some of their stuff is very orchestral-sounding, almost operatic (in a hard rock/metal context), and extremely complex musically.
I’ll give a third vote to E.L.O. and throw in YES.
Some **Tori Amos ** might fit the bill.
There’s a large body of work left by **Frank Zappa ** that one could wade through picking up orchestral-rock gems as one went along.
From the olden days, **Gentle Giant **(Octopus - the only GG album I have) and mid to late Jethro Tull (Songs From The Wood, Heavy Horses). The Who, for that matter - Tommy, Who’s Next.
If you want int’l bombast, there’s the **12 Girls Band ** and the Trans-Siberian Orchestra.
With Meat Loaf you’re bordering on Broadway Show type rock, which you might want to look into if you’re so inclined. Jesus Christ Superstar, Rent, Godspell, Hair, those sorts of things.
I don’t know about a full orchestra, but I think “Tonight, Tonight” by the Smashing Pumpkins features a string section. The video is very interesting as well.
I was wondering if this kind of stuff still gets made, as the rock I hear (college radio, too thrashy and classic rock) doesn’t feature much of it.
Hmm…I have heard other good things about Jeff Buckley on the boards…
I second Blind Guardian. Love 'em.