Breakdancing is what the media called b-boying (it's proper name). It originated in New York in the boogie-down-Bronx in the 70's.
EDIT no. 2: there are two schools of thought concerning breaking's origins. One theory is that it originated when east coast and west coast gangs taught themselves capoeira to defend themselves. this is believable since moves like uprock and toprock bear a striking resemblance to capoeira footwork. Others believe that James Brown's music had a bigger influence and so b-boying didn't come from capoeira directly. "Moves that we never saw before, like the capoeira moves, somehow ended up in breakin'." quoted from Mr. Wiggles in The Freshest Kids. "We've never seen capoeira, just like they never saw us dance. It definitely didn't come from another country; it was made up in the Bronx." says Mr. Freeze, one of the original members of Rock Steady Crew. Other influences include some of the old tap dancers like the Nicolas Brothers, and the Will Maston Trio. So if you want to be technical, Sammy Davis, Jr. was a b-boy.
Popping originated in LA on the other side of the U.S. Popping is a combination of locking and the robot. Though the east coast conceived breakdancing and hip hop, popping and locking, are respected parts of the family. Afterall, hip hop is all about sharing.
http://www.ukhh.com and The Freshest Kids