My favorite non-metal band is probably the Misfits. I don't listen to much other punk anymore except for the Ramones and Bad Religion. I also like the Sex Pistols' Rock N' Roll Swindle, mostly because it's funny.
The only alternative rock band I still like is Therapy?, a band from Ireland.
I'm really into neofolk/medieval/etc. types of bands, like The Moon Lay Hidden Beneath a Cloud, Ataraxia, Empyrium, Forseti, Ulver's acoustic album, Arcana, Mortiis... After listening to metal all day, it helps me get to sleep at night.