Bra-burning came to symbolize the feminist movement, but according to this article
at pressofAtlanticCity.com, the original 1968 bra-burning protest, that first associated bra-burning with feminism, never actually happened.
Members of New York Radical Women, upset by the Miss America Pageant's focus on women's physique and seeing an opportunity to publicize their cause, traveled to Atlantic City by bus. They wanted to burn things, as was in vogue then (people mad about other topics - such as the war in Vietnam - burned draft cards and flags), but city officials worried about the safety of the wooden Boardwalk asked the organizers not to burn anything, so they didn't.
Instead, the feminists dumped items like high-heeled shoes, bras, false eyelashes and issues of Ladies' Home Journal into a "Freedom Trash Can." They paraded a lamb outside Convention Hall and held up signs with such things as "Welcome to the Miss America Cattle Auction" written on them. Inside Convention Hall, demonstrators set off stink bombs during the pageant and unfurled a sign reading "WOMEN'S LIBERATION."
Newspapers helped fuel the fire. On Sept. 4, three days before the event, Lindsy Van Gelder of the New York Post wrote an article titled "Bra burners plan protest." In the Sept. 8 issue of the New York Times, protest organizer and former child actor Robin Morgan is quoted as saying the women would hold a "symbolic bra-burning." Open the next day's Atlantic City Sunday Press, and the headline jumps from page four: "Bra-Burners Blitz Boardwalk."
And so the bra-burning myth was born. Though I'm sure protesters must have burned their bras at some later point in time.