A cheap ticket called "Schönes Wochenende Ticket" (weekend ticket) is available from German train service. This ticket is valid on all trains and some buses in Germany. It can be used by five people to travel all-day-long from either Friday night till Saturday night, or from Saturday night till Sunday night. It costs 30 euros if you get it from machine, or 32 euros if you get it from the counter. This ticket is also valid in local buses and trams in some cities but not in others. Always ask from the local transport office whether it is valid inside the city. [1]
Every state issues a state-ticket (Land-ticket) costing 20-25 euros. This ticket is valid inside that state for the whole day (weekdays: after 9 am, weekend: from 00:00). Five persons can travel on this ticket. Some states also have a smaller version of this ticket valid for one person which is cheaper in cost. [2]
Another cheaper but less flexible way is travelling with other car-owners. Lots of people travel in such a way and is thus considered a safe method of travelling. The procedure is that people going from one city to another on their car advertise empty seats of their car on a website. These empty seats can be taken up by anyone. This method is usually cheaper than train and travel time is lesser. There are two popular websites for this purpose:
Mitfahrzentrale (no longer free-of-charge)
If you are tavelling with a high-speed train and one of the trains gets late, you can claim a portion of your ticket money back. Ask the DB counter in such an event. (Please enter more info).
There are many airlines that offer very cheap tickets (even a few cents, excluding airport taxes) to fly within Europe (and sometimes outside as well). Some of them are:
Ryanair: Starting from 0.01 euros, flies to numerous destinations in Europe. This airline operates from private airports some distance away from popular cities.
German Wings: Flies to many cities in Europe starting from 19 euros. Even flies to popular cities.
HLX: Costs starting from 20 euros, cheap airline flying to destinations in Europe.
Easy Jet: Another cheap airline flying to fewer destinations in Europe.
Air Belin: Yet another cheap airline.
Deutsche Bahn (German Railways) also offers cheap packages to Europe from time to time.
Remember that these costs are quoted without airport taxes. These taxes are always applied to tickets and may cost 10-50 or more euros.
The mitfahrer service mentioned above can also be used to travel within the whole Europe. Here again are the two websites:
Mitfahrzentrale (no longer free-of-charge)