Germany is a very safe country to travel to. Its crimes rates are low and the law is strictly respected. The most common form of a crime you’ll probably encounter is pickpocketing or bicycle theft.
Violent crimes such as homicide, robberies, rape or assaults are also not an issue in this country, especially not compared to most African and American countries. You might encounter pickpockets in large cities or at events with large crowds. Avoid crowded places, and apply extreme precaution when in public transportation or on bus or railway stations (airports, too).
You should also keep in mind that begging exists in some larger cities, and even though it’s not a serious issue, be careful and avoid getting into altercations with aggressive beggars, should they cross your paths. Some beggars are organized in groups.
Bear in mind that flashing any cardboard sign very near to your body could be a pickpocket trick, as well as attempts to distract you in any way.
You should also expect street demonstrations if your accommodation is in Berlin or Hamburg and if you’re traveling somewhere around the first of May. These demonstrations occasionally evolve into clashes between the police and a minority of the demonstrators.
Germany has experienced some terrorist attacks in the recent years and while you can't completely disregard the possibility of such attacks in the future, it is rather unlikely as the German government takes the neccesary security means of preventing any attacks.