As a student in Germany, you are automatically covered by an accident insurance for all activities related to the university including travel to and from the institution. The Studierendenwerk also provides an additional accident insurance in your leisure time, during work placements or other preparatory activities for your studies outside the university if such an accident leads to disability or death. This also applies for any such activities abroad. More information regarding all of these insurances can be found on the Studierendenwerk Ulm website.
Beyond this, you usually are provided with an accident insurance by your employer if you work during the semester or during the semester break. Associated contributions are paid by your employer.
In addition to health insurance, it is recommended to take out a private liability insurance policy. This covers compensation in case of any damages you cause accidentally (e.g. on your bike) or, sometimes, the loss of your flat or room key.