Some of these are "obscure"--others are simply underrated. Off the cuff, these are the first few that come to mind:
-Jeb Loy Nichols (a recent discovery, love his stuff)
-Imperial Teen
-Neko Case (especially her new album, 'Blacklisted')
-The Go-Betweens (most underrated band of the '80s)
-Freedy Johnston (especially 'Can You Fly' and 'Never Home')
-Amy Rigby (criminally overlooked)
-The Bottlerockets ('The Brooklyn Side' and '24 Hours a Day')
-Yo La Tengo (indie legends, deserve bigger following, especially recommend "I Can Hear the Heart Beating as One')
-Richard and Linda Thompson (both have done some excellent solo work, but their albums together are not to be missed)
And my personal favorite obscurity...Human Switchboard's album "Who's Landing in My Hangar?" To my knowledge, it is out of print and not available on CD (was released in the early 80's). Too bad. It is raw, intimate, deeply personal--just about the most uncommercial album imagineable.
There is so much good music out there that most people never get to hear. I am looking forward to the recommendations of others.