I'm going to second (or third, or whatever) the KEXP podcasts. That's probably my favorite radio station, so I'm a bit biased, but I subscribe to their Song of the Day, Live @ KEXP, and Music That Matters podcasts, all of which have introduced me to some great music that I otherwise would probably have never been exposed to. I used to subscribe to their Sonarchy Radio ("a live performance broadcast that showcases many northwest artists who are pushing the limits of music"), but after a while I just realized it wasn't for me.
I also subscribe to All Songs Considered, which is great. I really should subscribe to the Morning Becomes Eclectic, as I've got the first two CD compilations they released in the 90s, and absolutely love them.