I’ve asked this question before, but I’m constantly discovering older songs (I’m 24), so my list is always changing. Here are some of mine:

A Day in the Life – The Beatles
Gimme Shelter – Rolling Stones
Blue Bayou – Roy Orbison
First Day of My Life – Bright Eyes
Only Living Boy in New York – Simon & Garfunkel
Shelter From the Storm – Bob Dylan
(Sittin’ On) The Dock of the Bay – Otis Redding
Who’ll Stop the Rain – CCR
Blue in Green – Miles Davis
La Vie En Rose – Louis Armstrong
I Know There’s An Answer – The Beach Boys
China – Tori Amos
Hounds of Love – Kate Bush
Ripple – Grateful Dead
Hey You – Pink Floyd
Bold as Love – Jimi Hendrix
Not Fade Away – Buddy Holly
Watching the Detectives – Elvis Costello
Downtown Train – Tom Waits
Me and Bobby McGee – Janis Joplin
Behind Blue Eyes – The Who
Goodbye Yellow Brick Road – Elton John
Last Goodbye – Jeff Buckley
Bourbon Street Blues – Louis Prima
Both Sides, Now – Joni Mitchell
Baker Street – Gerry Rafferty
Jolene – Ray LaMontagne
Skinny Love – Bon Iver
You Got Me – The Roots
Slumdog Beautiful – OutKast