Stay On The Bike Path!!
If you're biking in Germany, following the rules of the road while biking will save you a lot of trouble dealing with everyone from the traffic police to the occasional civically engaged German grandmother. Unlike in most parts of the U.S., traffic laws for bikes are actively enforced in Germany, with the risk of getting ticketed being much higher than you might think. What do you have to look out for?
First and foremost, stay on the bike paths, or the side of the road if a bike path isn't available. Generally speaking, it's not allowed to be on the sidewalks (unless you're a small kid, in which case, good on you for getting into university at the age of about 10?), and you should remain on the bike path as much as possible. In the case of joint pedestrian/cyclist pathways, like those you might find along the Elbe or Rhein, stay on the right and make liberal use of your bike bell (you do have a bike bell don't you?).
As with cars, you are expected to have a front and back light once the sun goes down, and the German traffic police are not shy about ticketing you if you don't have them. If your bike doesn't have them, you can either wire some up with a dynamo for your bike tire, or use clip on lights that you carry with you. If you're using removable lights, its in your best interest to carry them with you, as though it's not the most common, light theft is not unusual, particularly in larger cities or more active areas.
If you are turning, make sure that you signal when you do. For those with their license, it's that thing they made you stop and stick your arm out the window to do in case your turning signals go out. German motorists assume that you are taking responsibility for signaling as any other vehicle on the road would do, meaning that if you suddenly turn without signaling, you are putting yourself at risk of an accident.