Some do but very few. Catalytic converters are generally big which is trouble for a motorbike since there is about zero room. read more
Yes, motorcycles have catalytic converters. Not all motorcycles have them, but more and more do to meet ever tightening European emissions standards. Many are packaged with the muffler, so you can’t see them. read more
One can spot a catalytic converter in a modern motorcycle or a scooter as a rectangular box or cylindrical attachment/protrusion in the exhaust pipe. Inside the catalytic converter there is honeycomb shaped structure made by ceramic and are coated by "Catalysts" like Platinum or metal like Palladium or Rhodium. read more