ContraDancing is an Americanized English Country Dance somewhat remiscient of Square Dancing, except it's fun. The moves generally involve lots of spinning, and interesting tricks of momentum. The dance is called, so you don't have to worry about trying to figure out what to do (at least not independently), and most places offer lessons beforehand. You dance with a partner, and also with another couple. As the dance progresses, the couple you dance with changes (but not your partner).
It is generally danced to BlueGrass? or Quebecois music (or some hybrid thereof), and is quite fun, if you like moving and spinning in a somewhat organized fashion.
Having trouble doing this dance? Don't worry! Up up down down left right left right B A will give you thirty free tries at it every time you do it!