I'd also note that some articles have been published recently about folk music, and while they weren't the reason why I threw this post together, they might be worth reading alongside my comments. Daniel passed along this piece by Hua Hsu, and I ran across this one the other day.
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Most of the music I listen to could be roughly classified as American primitivism or, perhaps more accurately and broadly, indie folk. The genre obviously has some old roots, but it's been reinvigorated over the past decade or two, most prominently by the film O Brother, Where Art Thou?, and probably by things like organic farming and microbrewing as new chic ways of convincing ourselves that we are more in touch with the land, or the past, or good ole' handi-craft-iness than we actually are (I say this as someone who falls for the self-deception as much as the next guy, as well as someone who finds the exercise formative even as it leaves some authenticity to be desired).
Indie folk is popular because it taps into a rich tradition, but I've also come to realize that it is commendable as an innovation in its own right. The celebrated music festival is aptly named Hardly Strictly Bluegrass. It's this hardly strict embrace of past artistic form that allows these artists to (I think, at least) be creative and even improve upon the work of past traditions for our present time.
Part of my realization of this has come from listening to those artists who have influenced the artists I listen to and being, frankly, turned off by their work. I love Dan Reeder's stuff, for instance, but can't say the same for John Prine even though Reeder was influenced by Prine, given a record deal by Prine, and often tours with Prine. The same goes for Gillian Welch (who is absolute gold standard as far as I'm concerned) and some of the early 20th century bluegrass and folk that influences her and often serves as material for covers in her touring and albums. Much as I want to embrace folk music culture in its fullness, some of the twanginess and hokeyness... really a lot of what's essential in the tradition... really turns me off. I used to think this was a problem with my own musical taste, but have come to the conclusion that folk doesn't have to be what folks of another generation made it. In fact, it's probably better if things do change. We always have the ethnomusicologists at the Smithsonian for recording earlier folksong, but new artists are here to follow the various muses of the day.
As an example, consider The Wind and Rain. It's an old song and has changed a good bit over time, and Gillian Welch has also recorded it. I'm not sure how earlier versions went, but here is Jerry Garcia and David Grisman doing it...
...contrasted with Gillian Welch:
The mood of the two versions is just night and day, and I think Welch is able to capture the ballad in a way that they aren't... a similar comparison is Garcia/Grisman and Steel Wheels doing "Shady Grove". Although I will say that sometimes earlier folk had a way of balancing a depressing story with a more lighthearted performance. Compare, for instance, Yoakam and Welch doing "Miner's Prayer" (or her own similar "Miner's Refrain"). Perhaps one benefit of earlier folk is that it isn't nearly so emotionally heavy as some of the more recent stuff can be. It's easy for an artist to sing about a miner's life in as morose and dramatic a way as possible... but someone who actually spends time in the mines might prefer a less depressing take on things at the end of the day. Here earlier folk singers might have hit on something that more recent versions simply reduce to over-seriousness.
Indie folk can also sometimes redeem the utter banality that is pop music... consider Iron & Wine and The Postal Service (There. Now I've offended all sides, and probably even Gillian Welch and Sam Beam themselves, since they thought it was worth using these earlier songs).
So I've mentioned a few artists already. Gillian Welch is worth pursuing, but also David Rawlings; any Welch album might as well have Rawlings on the title also, and vice versa for Welch's participation in projects that are nominally Rawlings's (Listen to "Ruby"). Old Crow Medicine Show is also closely connected with Welch and Rawlings through Acony Records, and while I'm not a huge fan of all of their stuff, they would be worth pursuing ("I Hear them All" is superb).
Lots of people know Iron & Wine, of course (listen to the best playing of "Trapeze Swinger" I've heard).
The Avett Brothers are also quite popular and associated with this genre, although some of their stuff is decidedly not folksy... which brings it away from my personal tastes but also shows how versatile and broadminded the new folk is. The Avett Brothers also seem to be a hugely friendly band- quite generous with their fans and always creating something of a family atmosphere (listen to "Murder in the City").
The Low Anthem is another one, and their single "Charlie Darwin" is worth listening to (the claymation is comparable to Fleet Foxes's "White Winter Hymnal")
Dan Reeder and Gregory Alan Isakov both have all of their work available for free listening on their websites.
The Steel Wheels is a great Virginian band headed by Trent Wagler; they have actually been doing a bike tour around the U.S., and there are some great youtube videos of their live performances from that (listen to "Red Wing").
The Everybodyfields has sadly split up for solo careers (and I've recently enough discovered the duo that I don't know anything about their after-lives), but their work is also quite good (listen to "Pontiac").