Youth Group does a good cover of "Forever Young" that I am probably going to use for my graduation next year (I just won the elections for next year's senior class pres.

)
These songs might not sound specifically like graduation songs, but when I make soundtracks I try to capture the emotion rather than specifically allude to the event. Ya know?
Youth Group: "Forever Young"
Yo La Tengo: "Bean Bag Chair", "Big Day coming"
REM: It's the End of the World as We Know It
Eluvium: Prelude for Time Feelers or Radio Ballet
Four Tet: Slow Jam
Rascal Flatts: My Wish
Do McLean: American Pie
Explosions in the Sky: Welcome Ghosts, First Breath After Coma
Belle and Sebastian: A Century of Elvis
The White Stripes: We're Going to Be Friends
Bob Dylan: Blowin in the Wind
I don't know if ANY of these will work out, but if they do, let me know!