EELS
Why does nobody ever mention the Eels? Daisies of the Galaxy is an almost solely acoustic album. Here's a list...
Daisies of the Galaxy - The Eels
Oh, What a Beautiful Morning - The Eels (great live CD)
Blinking Lights And Other Revelations - The Eels
Shootenanny - The Eels
The Ditty Bops - The Ditty Bops (while it's not indy, it's acoustic, and it's incredible)
Girls Can Tell - Spoon (beware, the rest is not acoustic. but it still rocks ass.)
Bryter Layter - Nick Drake
Also, the Sugarplastic have some great acoustic songs, but they're all scattered throughout their albums. "Resin" is their most acoustic album, but here are just some assorted Sugarplastic songs that are primarilly acoustic:
Folk
Little Teeth
Say Katie
Ohio
Please Mr. B
Novelty Man
Mercurochrome
Will
The Sugarplastic are worth a checkout from all fans of indy music everywhere. Best indy band ever.