Favorite non-metal bands?

Right off I have to admit I'm a huge Counting Crows fan. Cranberries. John Mayer (yeah, I said it). Weezer. Rush is my favorite band of all time.

I'll jam Carcass, Obituary, Archspire, Opeth, Aggalloch, Dismember, etc., but at some point I'll be listening to Rush or some other non-metal.

What faves do you have?