Cheap train travel in Germany - day passes
The Schönes wochenende ticket. The picture is from a few years ago, so now the price is a little higher.
Taking a train in Germany can be very expensive if one uses the standard prices of Deutsche Bahn - as expensive as in Norway. However, there are some offers that make make it much cheaper to take train there. Germans knows about this, the information is largely available in German on DBs web site.
The cheapest way to travel with train in Germany is to buy a "schönes wochenende" ticket. This cost 40 eur and is is valid in the weekend (saturday+sunday), and gives up to five persons possibility to ride one day with regional trains as long they want. This takes longer than express trains - but it is substantially cheaper since each person only need to pay less than 10 euro. To find connections, search Deutsche Bahn's website and mark for "regional trains only".
Since you yourself may not know 4 other people who are going the same direction, there is a website where you can put out offers for ride-share with train, or search for offers that others have created. This webiste - mitfahrgelegenheit - is also for shared ride in cars, but they have several people who put out offers for ridesharing with trains as well. And you can organize it yourself.
This make it possible to go to Berlin to Munchen, for example, for less than 10 Euro!
There is a similar ticket that is valid in weekdays as well - it is called "quer durch land". However, the price then is 40 euro for the first passanger, with each additional passenger paying 6 euro up to six passengers.
Link to schönes wochenende offer:
Deutsche Bahn (english)
Wikipedia (german)
Link to quer durch land offer:
Deutsche Bahn (german)