What are some really good rock bands?

I'm pretty picky about what rock I listen to. I don't like it too hard or screamo-ish. For example, I listen to Nickelback songs, such as Far Away. I also listen to a little bit of Breaking Benjamin, like Evil Angel and Breath. Those songs have just the right amount of rock for me. Judging by the songs I listen to, can anyone suggest some good rock bands...or songs? I need to add songs to my I-Pod that aren't country. :)