Hidden amongst all the mumbo-jumbo of Deutsche Bahn.....is the simplified all-day travel ticket. So, here is the deal.
One person - one price (44 Euro). Two people - one price (26 Euro a person). Three people - one price (20 Euro a person). Up to six people, but if you go this way......you all travel together.
Limits? Regional trains or U-Bahn/S-Bahn only. This takes out ICE (the high speed possibility). If you thought you could make it from Frankfurt to Berlin on regional trains in one day? Well....figure the high-speed deal to take roughly 3.5 hours. The regional deal? More likely to run up to twelve to fifteen hours.
How would maximize or use this ticket? You live in Stuttgart, and want to show someone downtown Frankfurt, and wind up in Wiesbaden for dinner, then travel back to Stuttgart on an evening train (getting back at 1AM). Total price for the day of travel? Fifty-two Euro for the pair.
Or you live in Stuttgart and want to head down to some fest which is a two-hour ride away....then return that evening on a 9:45PM train to stuttgart.
I would not recommend it for an event which is thirty minutes away by train.
Another good deal? The weekend pass, which allows you the same type deal, with kids under fourteen traveling with you free.