My muse needs to be fed. I always get good results with this kind of thing, so I'm throwing it out there. I want epic, super awesome music. So throw out your favorite band, hopefully one that's not mainstream (odds are I've already got it) and share the love.
I like stuff that has a good beat, but epic guitar riffs are cool, too. Songs like Thrice's Image of the Invisible, Pillar's Frontline, and Masterplan's Heroes are all examples of riffs I like. I don't like screamy stuff, for the most part; the song has to be really good for me to sit through "AAARGHBARGLEBLARGLEAAARH ANGST!" So, yes. The less of that, the better. Of course, if there is an edit of a song that lacks the screaming, like 30 Seconds to Mars's The Kill or Red Jumpsuit Apparatus's Face Down, I'm game for that. I like those songs a lot when they don't scream.
And yes, I'm already aware of Pandora. Unfortunately, I have a very hard time finding new stuff there. I'll get a couple, but most of the stuff I get I have to thumbs down because it doesn't sound anything like what I want. (You wouldn't believe the Euro-crap I've gotten on my E Nomine channel.)
I can give a sample of my playlist, in case it helps anyone else find new music or gives them an idea of what I like. Just because I have the band doesn't neccessarily mean I have a particular song by them. I'm kind of hoping this won't be a total crapshoot, in which I end up getting recommendations of what I already have. But we'll see.

qKumba Zoo - The Child Inside (Heh. Seaworld theme!)
Yoko Kanno - Information High (Macross Plus Soundtrack)
Franz Ferdinand - Take Me out
Gorillaz - Dare
Noir - Salva Nos (Good god, if awesome is a sound, it would be this.)
Linkin Park - Shadow of the Day
Michelle Branch - Set Me Free
Modest Mouse - Float On (Gah! The riff! I drool!)
The Killers - Human
White Stripes - Seven Nation Army
The Offspring - You're Gonna Go Far, Kid (Thanks, ~RabidChild!)
Deep Forest - Madazulu
Angels and Airwaves - The Adventure

A Youtube link is fine, but if you can't provide that, the song name and artist I'm perfectly capable of Youtubing myself.