Half Moon Rising by Yonder Mountain String Band, from the album Elevation.
Brown Eyed Women by The Grateful Dead. Pretty much any version, but I guess the Europe '72 version is the standard.
Windfall by Son Volt from the album Trace. It could have also been Tear Stained Eye from the same CD.
Tangled Up in Blue. This is a Bob Dylan song, but I'm specifically thinking of the Jerry Garcia Band version from the 1991 live album entitled Jerry Garcia Band.
Galway Girl by Steve Earle from the album Transcendental Blues.
What Deaner was Talking About by Ween from the Ween album Chocolate and Cheese.
To Live is to Fly. This is a Townes Van Zandt song, but I'm thinking of the Cowboy Junkies cover of this song found on their Black Eyed Man CD.
Good Guys and Bad Guys by Camper Van Beethoven from the album Camper Van Beethoven.
Ginseng Sullivan. This is a Norman Blake song and I love Norman's version from his album Back Home in Sulphur Springs. Of equal status is the Tony Rice take found on Manzanita. However, I would be omitting a primary booster of this song if didn't give Mike Gordon from Phish credit. I first heard Phish do it on a bootleg CD of their 12/31/93 show from Worcester, MA. I was already familiar with Norman Blake's music at the time and this connection sealed the deal!
Paradise by John Prine from his album John Prine. Honorable mention to every single other song from that same LP!
I must also list these five runner ups: A Horse in the Country by Cowboy Junkies, Golden by My Morning Jacket, Just Before the Evening by Leftover Salmon (Drew Emmitt), Truck Stop Girl by Little Feat (Lowell George), Desolation Row by Bob Dylan (as played by the Grateful Dead with Bobby spewing out the lyrics!), and In Tall Buildings by John Hartford.