Pick up Greatest Hits Vol. 1 (for the most famous early songs), Vol.2 (a better and larger collection of his best 60's songs minus the most famous), and Vol. 3 (later highlights).
Or, invest in one of his best albums: Highway 61 Revisited, Bringing it All Back Home, Blonde on Blonde.
Or pick and choose from the following:
Early "folk" period:
Talkin' New York
Baby Let Me Follow You Down
Don't Think Twice, It's All Right
Blowing in the Wind
The Times They are a Changin'
Lonesome Death of Hattie Carroll
Motorpsycho Nitemare
Mid 60's folk-rock period:
Subterranean Homesick Blues
Maggie's Farm
It's All Right Ma, I'm Only Bleeding
Positively 4th Street
It Takes a Lot to Laugh, It Takes a Train to Cry
Rainy Day Women #12 & 35
Visions of Johanna
Just Like a Woman
Late 60's "recluse" period:
All Along The Watchtower
I Dreamed I Saw St. Augustine
Lay Lady Lay
I'll Be Your Baby Tonight
If Not For You
70's
Tangled Up In Blue
Knocking on Heaven's Door
Idiot Wind
Isis
Hurricane
We Better Talk This Over
"Christian" Period
Slow Train Coming
Serve Somebody
Solid Rock
Heart of Mine
Groom's Still Waiting at the Altar
later stuff:
Jokerman
Neighborhood Bully
Brownsville Girl
Silvio
Political World
Ain't Talkin'