The de facto hymn of the counter culture was We Can Be Together by Jefferson Airplane.
Bands like the Grateful Dead were also very widely known in areas like Haight-Ashbury.
Strangely, people here are forgetting bands like the Jimi Hendrix Experience, which is also completely pathetic. Although Bob Dylan was influential, he wasn't nearly as important as Jimi Hendrix.
But if it's anti war songs you are looking for, then here are a few good ones:
We Can Be Together (Jefferson Airplane)
Give Peace a Chance (John Lennon and the Plastic Ono Band)
Machine Gun (Jimi Hendrix)
EDIT: And although War by Edwin Starr was a bloody good song, it is from the 70's and is Motown not 60's counter culture music.