If you're doing your Year Abroad in Germany you have 3 excellent tickets at your disposal, the Quer-Durchs-Land (QDL) Ticket, the Länderticket, and the Schönes Wochenende Ticket.
The QDL ticket costs 42€ plus 6€ per extra person (5 max (ie 5 on the whole ticket not 5 extra people)) and allows you to travel to anywhere in the country on regional trains (and S-Bahns which are run by Deutsche Bahn) spontaneously AND BACK (provided you're back by midnight). If it's a Werktag then it's valid from 9am to midnight, Feiertags it's midnight to midnight.
Länderticket is a smaller version of the QDL ticket; 21€ plus typically 3€ per extra person (5 max). It allows you to travel with regional/DB S-Bahns throughout a Bundesland (note only one Länderticket is required for Sachsen, Sachsen-Anhalt and Thüringen, ie Dresden, Leipzig, Chemnitz, Magdeburg, the Harz Mountains, Weimar, Erfurt, Oschersleben Motorsport Arena and many more are reachable with the same ticket). It is also valid from 9am to midnight, or for midnight to midnight on Feiertags/weekends.
The Schönes Wochenende Ticket is the same idea as the QDL ticket, spontaneous travel to anywhere in the country, but this one only costs 40€ plus no cost for extra people (once again 5 max), it's valid from midnight to 3 am the next day, so 27 hours (ie Saturday 00:00 to Sunday 03:00 or Sunday 00:00 to Monday 03:00).
Edit: This should probably just be titled Recommendable tickets in Germany. But oh welly. Travel option: Europa Park with all these tickets cost me 70€ from the other side of the country :P
Stick or dump?