I'll just throw some examples of my picks in. Halos: http://www.purevolume.com/halos (Listen to Amalgam or Pool Hall first) Good Old War: http://www.myspace.com/goodoldwar (Listen to Coney Island, Looking for Shelter, Just Another Day) Anthony Green: http://www.purevolume.com/anthonygreen (Listen to Slowing Down, Devils Song, Stone Hearted Man, Baby Girl) Love You Moon (Matt Embree of Rx Bandits solo project) http://www.purevolume.com/loveyoumoon (Last words of Nicholas Berg, Why popstars sell silicone) Tegan & Sara http://www.myspace.com/teganandsara (The Con, Back In Your Head, Call it Off, Nineteen)
If you like My Morning Jacket, Bright Eyes or M. Ward, the two main members of the first two and M. Ward formed a supergroup called Monsters of Folk. It's pretty damn badass. I think 3 songs are floating around on the internetz. Then you have bands already mentioned, like Iron & Wine, early Bob Dylan (Bring It All Back Home > "older" material), Sufjan Stevens, Neutral Milk Hotel, City & Colour... Then there are people like Townes Van Zandt (country flavored folk), Elliot Smith (not folk, but still fits what you're looking for), Kaki King (female instrumental guitarist, really chill stuff), Vampire Weekend, TV on the Radio, Mew, the Silversun Pickups... I could go on all day, really. This is the type of music I mainly listen to these days.
Band of Horses: not all acoustic, but it's definitely souful, catchy, soft. Attack In Black's last two records are acoustic, check out their first record too, it's all genius. The Avett Brothers, don't think they were mentioned in here yet. Bright Eyes/Conor Oberst's "solo" records Two Gallants Andrew Bird Belle And Sebastian Fences: haven't released a lot, but the stuff that's out is great Jack Johnson: pretty good, easy listening Kevin Devine Curtains by John Frusciante and his other acoustic stuff, others stuff is also brilliant, though The Modly Peaches Paul Baribeau (More stuff of Plan-It-X Records: Defiance, Ohio / Mischief Brew / Andrew Jackson Jihad / Wingnut Dishwashers Union / ...) But definitely check out the aforementioned: City And Colour, Tegan and Sara, Sufjan Stevens, Neutral Milk Hotel, Fleet Foxes and Frank Turner.