My favorite 60s band is Canned Heat, they started out as a blues cover band and eventually developed their own unique style. Their song "Going Up The Country" was the Woodstock theme song.
EDIT: I forgot my favorite 70s bands, Kraftwerk and Led Zeppelin.
Boston, Kansas, Styx, Strawberry Alarm Clock (okay, so I only know the one song), Aerosmith, the Beatles, the Steve Miller Band, Jefferson Airplane/Starship... there are more but my mind's ready for bed :\