While I appreciate some, I don't feel like I'm enough of a musician, or that I am musically inclined enough to appreciate the how/why of what they're doing. I would just be listening for the reason that it isn't pop music.

Maybe that's why I like The Decemberists. Not super-intricate, musically, but they do find ways to be interesting otherwise. Like their 9-minute sea-shanty about a boy seeking revenge on his deadbeat, seafaring father. (www.youtube.com)