Is there a reason most police departments have officers who ride motorcycles? You can’t transport a person in custody on a motorcycle. However, motorcycles are more easily hidden for speed trap enforcement. I believe this is the primary use.
The only advantage I can see for a motorcycle over a squad car is that a motorcycle can weave through traffic if there is a serious accident which has brought a freeway to a complete standstill. The motorcycle can split the lane and reach the scene of the accident.
Last summer the local police department here in Bloomington started using motorcycle cops for the first time. The press release from the mayor, in the newspaper, said that having motorcycle police, among other things, would help the image of the police department, and make them seem closer and more visible to the average driver instead of being hidden away inside a cruiser. I think there’s also the fact that they just look cool, and people like things that look cool. The police motorcycles here are white and blue Harley-Davidson Police Specials and are always immaculately polished and shiny, so they’re just cool to look at.
What Friedo said, but not just in big heavily-congested cities. Motorcycles can get through and around accidents, traffic jams, construction debris, and other things that cars can’t. Also, when in an area where cops can work solo (i.e., you don’t need two traveling together), the motorcycles are cheaper than cars, get better gas mileage, and take less parking space at headquarters or the police garage.
That is exactly the reason why the UK has motorcycle police. In heavy traffic, motorcycles can reach a trouble spot much more quickly. There are some paramedics in the UK who use motorcycles for the same reason.
I used to live in a city where they had two kinds of cops: normal ones on duty in Chevrolet Tahoes and the ones on traffic duty on BMW motorcycles… I noticed they especially liked the motorcycles for running radar as it was much easier to be hidden (especially in comparison to the SUV). Motorcycles can easily hide behind pillars under highway overpasses too. In general, its better for radar and maneuvering through congested areas and doing general traffic-related work.