List of my favorite folk bands/artists
 

The Avett Brothers: They play folk rock complimented by their impressive lyricism. Some of their songs sound influenced by grunge or punk, others even pop, but normally the songs use folk instrumentation.

The Head and the Heart: I don't know much about this band, but I like their new style they bring to folk music.

Dan Mangan: This artist is more rock than folk, but I wanted to include him anyways. He has a more down-to-earth sound while not sounding generic, and he never fails to entertain both folk and rock listeners in his songs.

Chris Thile: The best mandolinist alive and a superb songwriter, Chris Thile writes everything from progressive bluegrass to classical and jazz.

Some of my other folk bands I like include Dawes, Trampled By Turtles, The Wood Brothers, Chatham County Line and Blizzen Trapper.

The Dubliners are pretty awesome

I love them all. Country songs are relaxing music.

In no particular order:

Bob Dylan
Joni Mitchell
Jackson Browne
Mark Knopfler
Robert Plant
Emmylou Harris
Gillian Welch
Kate Rusby
Van Morrison
The Waterboys
Beth Orton
Cara Dillon
Ruth Moody
Stepehn Fretwell
Seasick Steve
Eliza Carthy
Naomi Bedford
The Chieftains
The Dubliners
Damien Rice
Lisa Hannigan
Karine Polwart
Julie Fowlis
Iris DeMent
James Taylor
Teddy Thompson
Richard Thompson
Thea Gilmore

Not everyone on that list is a 'pure' folk artist, but have dabbled in it to varying degrees.

Are Johnny Cash's American Recordings also considered as folk? Since they are some kind of Americans, I would like to mention them too.

Saw someone mention Eliza Carthy, great artist.

John Martyn, Terry Callier, Robyn Hitchcock, Chris Thile, Duncan Sheik, Gordon Lightfoot, Noah Gundersen, Linda Perhacs, Sturmpercht, Nico, Douji Morita, Tim Buckley

I like Band of Horses.

Alela Diane
Clarence Ashley
The Doc Watson Family (that album got me into folk music)
Third Ear Band
Jack Rose
Six Organs of Admittance
Marissa Nadler

The Avett Brothers are amazing! I also love Mumford and Sons..Bob Dylan, Emmylou Harris, Johnny Cash, Joan Baez, The Head And The Heart, James Taylor, etc..