No, seriously though, screamo vocals are a fairly recent invention. They get on my nerves a lot. And I take it you're not looking for guttural death metal or croaky black metal either, so thrash and traditional metal might be your best bets. Here's a few suggestions (some of these might be obvious, but you didn't give us a big list of what you already know!):

Anthrax (both vocalists are excellent)

Accept

Annihilator (quality can vary wildly between albums)

Bruce Dickinson's non-Maiden solo material

Candlemass (can be almost operatic at times)

Cathedral

Crash (Korean thrash, sometimes quite similar to Metallica)

Dark Angel (heavier end of the thrash spectrum, and the vocals can be a bit harsh at times)

Death Angel (There's some awful screams on the first album, but after that the vocals are excellent)

Devilskin (NZ metal with a female singer. One of the biggest bands in the country)

Diamond Head (Oldie but a goodie. Lars Ulrich's favourite band)

Dio. Dio. Dio.

Dragonforce

Dream Theater

Exodus (Vocally the first album isn't very polished, but is very enthusiastic! Can't go wrong anywhere with this band)

Faith No More

Fight (Rob Halford without Judas Priest)

Flotsam & Jetsam

Forbidden

Helloween

Iced Earth

Judas Priest (but you must know these guys already, right?)

King Diamond (very high pitched vocals)

Manowar \m/

Nevermore

Nuclear Assault (Try the song Butt Fuck for a mix of metal and blues!)

Oliver Magnum

Overkill

Onslaught

If you're looking for metal/hard rock mixed with blues, you might want to check out some stoner rock/metal bands. Here's some that I would recommend:

Clutch (Not really metal these days, but they sure deliver some of the best heavy blues there is.)

Sleep (Black Sabbath-inspired stoner doom.)

Queens of the Stone Age (Less metal, more hard rock, but their first 4 albums are great. The 4th one is probably the most blues-oriented.)

Sorry for Nothing (Their second album is full of influence from Motorhead and Black Sabbath.)

Witch Charmer (Doom-y Sabbath-esque metal with great female vocals.)

And of course the aforementioned Cathedral.

If you like grunge, then Soundgarden has some great bluesy and heavy stuff.

Hope all these recommendations aren't too overwhelming. 

Symphony X

Lynch Mob

Badlands

Avatarium

Armored Saint

Helstar

Vicious Rumors

Racer X

Savatage

I definitely second those as well, especially Helstar which is one of my favorite bands. 

Kamelot 

Falconer

Nightmare

Dark Forest (The UK one)

Pyramaze

Armory

Metal Church

Argus

Crimson Glory

Paradox

Vainglory

MorningStarlett

Sinbreed

I could probably name more, but that should get you started along with everything else mentioned.

I bought the King Diamond five album box set this year. It was a long time overdue for me. There's the odd weak track, and some of the concept stuff comes over a bit cheesy, but mostly very solid metal.

King Diamond cheesy? Really? Then what do you call most European power metal like Rhapsody (whichever it may be) - cheesy deathly overdose?

 I can't take bands like Rhapsody too seriously. Love the musicianship, but the flamboyance is just too over the top for me.

Morgana Lefay is so much more than just power metal, it's thrashy and groovy at times, nothing cheesy about that. They could sing about kittens and rainbows and still it would not be cheesy.

Same with Tad Morose. I listened to an album from a band called Inmoria (Invisible Wounds - 2009) who had members of both bands and sounded great.

I do enjoy some Stratovarius and Thunderstone every once in a while, it's a bit cheesy but it's bearable. Same with some hair metal bands.

Any other recommendations keep them coming