Bucking Bikes aka Eccentric Wheel Bicycles make the rider look like they are on a bucking bronco. The eccentric wheels cause the bike to move in an up and down elliptical pattern which mimics a bucking bronco.
Bronco Bike from Randy and Nova's Bicycle Scrapbook
The Hula Bike from Bicycle Forest is a variation of the Bucking Bike. Instead of a conventional drivetrain, the Hula Bike uses an eccentrically laced rear wheel which allows the bike to be propelled by hopping up and down with the right rhythm.
The Hula Bike from Bicycle Forest