Acoustical music

Also... If you like jam bands, Widespread Panic's Live Wood is completely acoustic & very good. 

Most Bluegrass music is all acoustic, and generally better recorded than Rock ta boot. Look for Chris Hillman’s (bass player in The Byrds, but he was in Bluegrass group The Hillmen prior to that) albums on Sugar Hill. For incredible live recordings of Church choirs, look for Bob Fulton’s recordings on the Ark label (out of Minnesota in the 1970’s)---astoundingly lifelike, every individual, delicate voice clearly audible. His recordings also contain some of the most massive pipe organ sounds I've ever heard. Speakers (or subs) capable of reproducing the bottom octave definitely required!

Conemporary folk music on the peerless Stockfish label.  Just buy their first Closer To The Music sampler SACD.  A real "You are There" or in some cases "They are with you" experience.

Pretty much everything in my collection...if you are in the northeast, PM me and you can come over.  Hundreds of good examples...I focus on the music first vs the recordings, but look at these artists:
Lyle Lovett
Eddie from Ohio
Eva Cassidy
Emmy-Lou Harris
Will the Circle be unbroken 1, 2, 3
Anything by Mark O'Connor.  Classically trained violinist with very strong jazz and bluegrass crossover. 
Skip. Hop and Wobble
David Grisman (if bluegrass/jazz fusion is not your thing, try Grisman and Kobialka- Common Chord)
Vienna Teng
Wailing Jenny's 
Some of Keb Mo's stuff is acoustic,
Jorma Kaukonen (guitar half of Hot Tuna) has a solo acoustic blues album.
Richard Thompson for sure. 

+1 for "Eddie from Ohio"