The ICE (Intercity-Express or InterCityExpress) is a high speed long-distance train that connects major German cities with each other and with cities in mostly neighbouring countries. At a speed of 300 km/h you can travel to Austria, Switzerland, Belgium, France, or Denmark, for example.
The EuroCity and InterCity trains offer long-distance connections between European and German cities, respectively. There is also a high number of regional trains connecting bigger as well as smaller cities in Germany.
Fares can vary depending on the service you choose, but in general are not cheap. A seven-hour ICE train ride between Berlin and Munich, for instance, would be € 130. As a rule, the longer the distance is, the higher is the fare. Sometimes, however, going by train can be more expensive when travelling within smaller regions than between cities.
There is also a great number of national intercity coaches, connecting many German cities, and some international intercity coaches.
See the Deutsche Bahn website for more information: www.bahn.com.