I’ll toss in a couple of slightly more obscure British bands from the 70’s - Camel and Nektar. More prog than orchestral, but definitely worth a listen. In particular I would highly recommend Camel’s “(Music inspired by) The Snow Goose”, or Nektar’s “Remember the Future”.
Try Deep Purple’s Concerto For Group And Orchestra: it’s a live recording at the Albert Hall of a full-length concerto written by Jon Lord for the band and the Royal Philharmonic. I think it was first performed in 1969, when that kind of ambitious experimentation was de rigeur, and it’s received mixed reviews over the years, but for my money it’s a classic, and breathtakingly accomplished.
Yeah, most of the bands I mentioned don’t get much radio play. Radiohead does of course, but they’re probably the farthest from what you’re looking for in my list. Still, if you like a great sense of melody and a powerful sound, you’ll probably enjoy post-Buckley Radiohead.
I think Spiritualized might be the closest. Find Ladies and Gentlemen We Are Floating in Space. It’s in my lifetime top 10 or so, along with Jeff Buckley’s Grace.
Disarm also has strings, but not as many.
November Rain by Guns & Roses has an orchestra, at least in the version they did at the MTV awards. Also maybe Don’t Cry. Both are from the album Use Your Illusion.
William Shatner’s Common People doesn’t have an orchestra, but the title track has a huge chorus, made up of audience members at an early concert.
Kashmir by Led Zeppelin was recorded with an orchestra, at least in “Puff Daddy”'s version, and maybe others.
Mike Keneally and the Metropol Orkest, The Universe Will Provide . The link is to AMG’s review of this 2003 work, which is one of my all time favorites. Keneally was a Zappa protoge, and his work is all over the board. But you need to check this thing out.
Get XM Satellite Radio and listen to Channel 40 - Deep Tracks. I hear this stuff all the time driving in to work in the morning.
You might also want to try:
Godspeed You Black Emperor
Explosions in the Sky
Muse (more “pompous” than “orchestral”, but what the hell)