Sarah writes about Berlin-Munich: "If we had a car I was thinking of stopping at Dresden..." "I think if we were to take a train we would probably not stop and just get there in one trip."
You should have no need fear of being "railroaded" all the way to Munich! You can make your stopovers by train. Here's what I suggest for a 2-day trip to Munich with stopovers...
Day 1: Use the regional trains to travel to Dresden (about 3-3.5 hours) on a "Quer durchs Land" ticket (daypass, weekdays, €52 for two) or a "Happy Weekend" ticket (daypass, Sat or Sun, €44.) If there are places on the way you want to visit, just hop out and get back on a later train for Dresden or wherever you change trains next. The daypass allows you to do this.
Day 2: For the longer trip from Dresden to Munich, buy an advance-sale savings fare - best price for two is €49 if you buy in advance and pinpoint your travel time and date. You can schedule a stopover somewhere interesting on the way - like Nuremberg, for example. The DB site allows you to do this quite easily. I just tried this for a sample date in March (20.03.2015)
Lv. Dresden 7:53
Ar. Nuremberg 12:19
Lv. Nuremberg 16:27
Ar. Munich 17:39
Drop your bags in a locker at Nuremberg station while you enjoy the town.
You can play around with the schedule a lot and get the same €49 fare. Plan to stay longer in Nuremberg? You can schedule a later train and get to Munich at 18:41, 19:41, 20:41, or 21:39, all for the same price. Also, if the trains that get you between Dresden and Nuremberg are REGIONAL trains (and I think they all are on this route) you can leave Nuremberg any time you want in the morning - your savings fare ticket binds you ONLY to the fast trains on your schedule (in this case the one between Nuremberg and Munich) and allows scheduling flexibility on the routes covered by regional trains. So for two, your two-day trip cost is about €100.
There are other towns you might visit instead - Nuremberg is just an example.
If you do this route by car, it's 655 km and about 8 hours of driving time - figure nearly €80 for gas alone. A 2-day rental fee on top of that will not be cheap, nor will insurance. And then there are parking fees, insurance, the potential for car dings (or shady rental agents that bill you later,) traffic delays, traffic violations, and all the other fun that comes with a car. Instead you could be sipping your favorite German beer on the train.