These are not in any particular order:
John Denver - I said they weren't in order, but I have to start with numero uno... One of my father's favorites became one of mine once I became an adult. As Lindsay said, "It is physically impossible to stay angry while listening to a John Denver album. It is just so damn uplifting and soul-settling!"
Union Station - Many of you probably like a song by these guys but didn't realize it: The Soggy Bottom Boys from O' Brother Where Art Thou... Most of their stuff is labeled as Allison Krauss & Union Station.
Levon Helm - Singer/Drummer from The Band. His solo stuff is very gritty, mountainous and homestead feeling. You can't beat his raspy voice either.
Dave Carter & Tracy Grammer - Probably my number two. A brilliant mix of country & folk with a twang and a Buddhist or old-west theme through much of it.
Neil Young - There is so much of his work out there that you can compile a full album of songs that have the feel to them (which I have done multiple times).
Tom Russell - Hailed as one of the best songwriters out there by many. Western music and ballads are his specialty. Lindsay loves him more than I do, but you should definitely check him out.
Ryan Adams - Kind of the same situation as Neil Young. A lot of his stuff has a good organic feel to it, and then some of it does not... But overall he usually has several songs that make it onto my mood music CDs.
There are many more that contribute a song or two: James Taylor, Joan Baez, Townes Van Zandt, Tom Petty, Steve Earle, Old Crow Medicine Show, Johnny Cash, Hem, Buddy & Julie Miller, Drive-By Truckers, Emmy Lou Harris, etc.
PS: I almost forgot about one of the main ones...
Gillian Welch - If you want Americana and a homesteadish feel you have to listen to her.