Nina Nastasia, one of my favourite artists - get any or all of her albums, they're all excellent, although probably best to start with The Blackened Air or On Leaving.
Diane Cluck O Vanille/Ova Nil is a great album, the harmonies are amazing (obviously impossible to reproduce live when it's just her, but I recommend a listen).
Couldn't find a suitable clip on YouTube, but Tanya Donnelly's last album, Whiskey Tango Ghost, is a lovely sweet collection of acoustic songs.
First album by The Evens is great (again, I couldn't find a clip on YouTube that wasn't marred by hideous sound quality) - they're a sort of punk folk outfit comprising Ian Mackaye (ex Fugazi and Minor Threat) and Amy Farina. Intricate, thought-provoking songs.
Low are probably my favourite band, if I had to pick one - they've been making quality slowcore for many years and there is a wealth of gorgeous acousticky music to choose from in their back catalogue. The live clips on YouTube don't really do their sound justice, but still: Two Step, When I Go Deaf, Sunflowers, Murderer, Point of Disgust. Things We Lost In The Fire is a good place to start, it's a fantastic, beautiful album.
I love this song, but the original version by Jackson C Frank.