I've been thinking this over for a while. This is probably my final answer, at least today. Excluding Jazz and Classical.

Imagine - John Lennon
Mr. Skin - Spirit
The Wall - Pink Floyd
The Dutchman - Steve Goodman
Harvest Moon - Neil Young
Some Velvet Morning - Nancy Sinatra and Lee Hazlewood
Goodbye Yellow Brick Road - Elton John
Suzanne - Leonard Cohen
I've Been Everywhere - Johnny Cash
I Am a Man of Constant Sorrow - Soggy Bottom Boys
Mustang Sally - Wilson Pickett
Angel from Montgomery - John Prine
Big Yellow Taxi - Joni Mitchell
Tell Mamma - Etta James
Freedom (opening song at Woodstock) - Richie Havens