Not all means of transportation are created equal.
Different countries use different means of transportation, and same transportation varies in different countries. Sounds complicated? Let's try again.
Trains in different countries differ dramatically from one another. For instance, the interior of some trains in Denmark look like the interior of airplanes; high end and spotless. A train in New York however, is a totally different story.
For longer communes, people in the States use long distance buses and airplanes, if they don’t want to drive. For short distance, they tend to prefer taxis instead of buses or underground trains which are also popular nevertheless. There are exceptions of course but in New York you will see more people using yellow caps than any other means of transportation.
Black taxis are also a good option for London if you can afford it. Mini cabs are also available in London but be very careful with this service. They are not licensed and you probably do not know what you are getting into.
Trains are a good way to get from one place to another in a lot of European cities especially Nordic countries, UK and Japan. In London and Paris, most people take the underground to get around or the bus in the case of London. With so many Big Brother cameras everywhere, the feeling of safety is reinforced.
In Copenhagen, people walk or bike. Mostly they bike. There aren't a lot of cars and no traffic jams. And they do have the cleanest and newest trains you can find.
You can always visit the local tourist information office and find out the best and safest way of getting around in the area.