Stan - Eminem
Yellow Brick Road - Eminem
8 Mile Road (Kind of. Although I guess it could be considered autobiographical he's mainly speaking from the point of view of the character Jimmy) - Eminem
Get Down - Nas
One Love - Nas
Rewind - Nas
Ballad of Worms - Cage
Stripes - Cage
Student Body - Kristoff Krane
You Never Know - Immortal Technique
Chris Dolmeth - Hopsin
In My Sleep - Joe Budden
Pray For Me - Joe Budden
Exxxes - Joe Budden
OutKast - Da Art of StoryTellin' (Andre 3000's Delivery

)
The Boy With No Name - Bop Alloy
In Her Music Box - Atmosphere
The Waitress - Atmosphere
Hair - Atmosphere
Adventures of Larry & Tina - Wax
No Strings Attached - Dumbfoundead
Come to think of it, most of my favorite songs are based around story telling.