Come Away Melinda was written by Malvina Reynolds. Kind of anti-apocalyptic rather than anti-war in the pre-nuclear sense...
Where have all the Flowers Gone?
The Minstrel Boy was probably the first song I came across back in the 1950's that struck me as being anti-war. I remember finding it in my grandmother's piano bench, picking out the melody and reading the lyrics and getting quite upset.

Jimmy Newman by Tom Paxton.
But The Band Played Waltzing Matilda is a stunner. My first time hearing it was Joan Baez's version.

Strafgod <-- apologizes if he's broken any posting rules or etiquette, having just bounced in from a posting on rec.music.folk and, intrigued by the thread, just went ahead and posted without the requisite lurking, reading the faq, and paying proper attention to the rest of this great site!