I love the sounds of artists/bands like Sufjan Stevens, Andrew Bird, St. Vincent, Grizzly Bear, Anathallo, etc..sort of has a modern classical feel to it while still being indie.  Live performances by these guys are usually incredible.  not exactly the same but Beirut is also amazing, gypsy flavored folk music.

Edit:  oh, I was supposed to list albums here.  These artists have multiple albums so i'll list my favorites

Sufjan Stevens - Illinois.  Should be one of the starting points of those looking to get into indie/folk/whatever music.  And clocking in at well over an hour, it's pretty epic, too.  The album itself is dedicated to the state, Illinois if you couldn't tell.

Andrew Bird - Noble Beast.  I compare him to Sufjan a lot although Bird's sound is more rocky at times.  I've actually not yet to see him live because tickets are expensive yet sell out within hours/days.

St. Vincent - I can't pick a favorite album from her.  Get all 3:  in chronological order it goes, Marry Me, Actor, and Strange Mercy.  Marry Me was a solid, adventurous debut but I feel like she hit it out of the park with Actor.  Honestly she doesn't get as much credit as she should!  Strange Mercy was phenomenal too; it scratched my top 3 of 2011.

Grizzly Bear is my favorite indie band.  They solidified their position when I saw them live a few years ago, right after Veckatimest got released. They were on tour with Beach House (side note:  Check out Beach House too!) and they blew away every single expectation of how I thought they would sound live.  Overwhelming amount of clarity, the cleanest, clearest instrument separation, seriously you could have cut it with a knife.  For just being four guys they worked hard to faithfully recreate the music on the record and, well, I ended up going home very disappointed because from there on out, I felt the albums sucked compared to their live show.  But oh well 

Anathallo - Floating World.  I like to pair this album next to Sufjan Stevens because of similar feel.  Except Floating World has this whole Japanese folklore thing going for it in the lyrical content. Very enjoyable.

^ The above post suffers from genius overload. :D

"Contemporary folk" in itself is a very broad affair. It covers everything from the likes of Pete Seeger over numerous talented people of the '60s and '70s, Suzanne Vega in the '80s and '90s (pretty consistently good btw) to present-day UK "NuFolk" à la Laura Marling and Emmy the Great. Let's stick to the latter for the time being.

I don't think one can really go wrong with any of Laura Marling's 3 albums, even though it is apparent how she has progressed over the years (the first one came out when she was only 17). Sound quality tends to be fairly good. Oddly, the CD version of her second one was apparently mastered from a vinyl rip.

I really enjoyed Emmy the Great's second album Virtue, which is a contemplative affair somewhere in between her earlier stuff, Suzanne Vega and St. Vincent (really a lot more singer/songwriter than folk overall), with some Laura Marling and Priscilla Ahn thrown in. Generally decent sound, though I did notice a few small studio glitches.

Somewhere in between pop and singer/songwriter there's Tina Dico from Denmark (at least that's the name she uses internationally, in her home country she's known under her real name of Tina Dickow). Previous releases seem rather mainstream in loudness levels (read: loud), but her latest live CD/DVD with the Danish National Chamber Orchestra isn't. (Apparently recording with an orchestra currently is sort of an "in thing" after the likes of Sting and Peter Gabriel did it. Listening to "True North" on her YT channel, it seems to work pretty well in this case.)

Bon Iver - For Emma, Forever Ago

Wilco - Yankee Hotel Foxtrot

Iron & Wine - Kiss Each Other Clean

Feist - Let it Die

Fleet Foxes - Self Titled

City and Colour - Little Hell

Beirut - The Rip Tide

Blind Pilot - We are the Tide

Keep em coming, great albums thus far. 

Wow some great bands/albums have been named already! Well here are my additions.
Angus & Julia Stone- Down The Way
Bright Eyes- I'm Wide Awake It's Morning
Bright Eyes- Fevers and Mirrors
DeYarmond Edison- DeYarmond Edison
Right Away, Great Captain- The Bitter End
Kevin Devine- Split The Country, Split The Street

Whitley- Go Forth Find Mammoth

Josh Ritter - The Animal Years

Joe Pug - Messenger & The Nation of Heat EP

Leonard Cohen - Old Skin for the New Ceremony

The Tallest Man on Earth - Shallow Grave & The Wild Hunt

Strand of Oaks - Pope Killdragon

Langhorne Slim -  Self-titled & Be Set Free

Every Gillian Welch album

Mark Olson & Gary Louris - Ready for the Flood

Bonnie 'Prince' Billy - Lie Down in the Light

Townes Van Zandt - Live at the Old Quarter