Besides metal I mainly like hard rock and industrial with the occasional neo-folk band thrown in for good measure. Anyway here's a few non-metal bands I find enjoyable. Fleet Foxes (neo-folk), Mattafix (reggae), Diary of Dreams (darkwave/industrial), Alice in Chains (grunge), Antimatter (ambient/melancholy rock), Pain (Peter Tagtgren's other band kind of pop influenced hard rock/industrial pretty interesting stuff!), Thieves & Liars (80's influenced rock), Kings of Leon (hard rock), Poor Man's Riches (Christian hard rock), Rotterdam Terror Corps (gabber), Dead Can Dance (experimental folk) and of course the classics like Nazareth, Bob Dylan, Jimi Hendrix, and Steely Dan.
Joel