Tickets are not checked on the bus and subway. Fare enforcement is done by NYPD, the local police department consisting of police officers.
Tickets are checked on the commuter rail, but conductors only really are empowered to ask people to pay the onboard fare, which is higher than purchasing a ticket at a machine or at an office outside the train. Conductors can call police, but are not able to make arrests or use physical force to remove farebeaters from trains.