Folk, Folk-Rock and acoustic music in general are some of my favourite kinds of music. I've mostly listened to newer stuff and I seem to find worthwhile music of this kind quite often.
Some older stuff:
There's Bob Dylan of course. I only got a compilation album so far. Might get into his music a bit more sometime.
I really like Pink Moon by Nick Drake. Five Leaves Left and Bryter Layter have yet to impress me as much.
Bon Iver has a few good songs and For Emma, Forever Ago is overall a pretty good album which sets a pretty strong atmosphere.
Bonnie "Prince" Billy's (aka Will Oldham) music leans more on Americana and I absolutely love his album I See a Darkness. One of my all time favourites. I have yet to check out his other works.
Erland & The Carnival is a very recent find for me. Their self-titled album sounds quite a lot like 60's folk music I think. There's even a few cover versions of old folk songs.
Fleet Foxes was mentioned above Rock N' Rollin' Man. Their s/t debut is a great album. Sun Giant ep also contains some very good songs. They got a new album coming this year.
Iron & Wine (aka Sam Beam) is one of my favourite artist in this genre. The earlier stuff is more acoustic (Our Endless Numbered Days for an example) but he has started to include more and more elements into his music with the two following releases The Shepherd's Dog and Kiss Each Other Clean which was released earlier this month. I actually prefer his later material because it seems to offer more things to find.
Junip was another new artist I found out about last year. Their music is a mix of acoustic guitars, interesting rhythms and 70's kind of synths. Fields is a good album even if it's a tad bit too samey.
Junip brings me to Jose Gonzalez who is the frontman of the band. He's been pursuing a solo career too. I've only listened to his first album Veneer once but it seemed like a quality, barebones folk album.
And then there's of course one of my favourite bands Midlake. Their second album The Trials of Van Occupanther is a soft-rock / folk-rock type of thing which I love. Their third album The Courage of Others is heavier and darker. I've read comparisons to Jethro Tull and Fairport Convention.
The Tallest Man On Earth was also mentioned above by Rock N' Rollin' Man. He sounds a bit like Dylan but after some listening you notice that he's certainly not some cheap rip-off or anything. I've only listened to Shallow Grave so far and the melodies are so catchy that I wonder why he has yet to gain bigger success. His second album The Wild Hunt was released last year.
I'm interested in seeing what this genre offers in the future and to explore some of the old classics.