Cars that are not privately owned by people that drive them themselves, but by (usually smallish) companies operating them. I.e., there's a driver inside who will drive you wherever you want to. If everything works out, he will charge you by the kilometre for the distance traveled, if it doesn't work out, he may rape and/or kill you. Taxis are also called cabs resp. taxi-cabs. In Germany, they're beige, in the U.S., usually yellow. Nearly all German taxis are Mercedes-Benz diesels. Older ones thus often emit gruesome noises that can set your teeth on edge.

While in New York, every third car is a taxi-cab, and you just need to wave your hand to make one stop, in Germany you need to give the taxi company a call or go to a special parking lot where lots of taxis wait around, bored drivers inside reading the BILD-Zeitung. On the other hand, German taxi drivers usually speak much better English than New York taxi drivers. For information on German taxi drivers in New York, watch Jim Jarmusch's film Night on Earth.