Germany is a place where women can feel fairly safe. While no place is able to say it is completely safe for women, Germany is among the top places they are, generally speaking. One reason is that the law in Germany is strictly enforced. It is the 14th safest place in the world according to statistics. Cabs and transportation are said to be safe, for the most part, for women to travel with, even alone.
There are organized pick-pockets and such so one should be careful whether male or female. There are also terrorist threats in the country. For the most part though, women are as safe or safer in Germany as in most places in the world.