EU-Citizens with a European Health Insurance Card have also coverage in Germany. Non-EU citizens are required to purchase statutory health insurance to enrol at a university. Exceptions: Students taking German courses, students at the Studienkolleg, PhD students as well as students older than 30 years of age, or who have studied for more than 14 semesters generally buy private health insurance.
If you have to/want to buy private health insurance please note that the efficiency has to be equivalent to the health plan of the SGB V (Sozialgesetzbuch) parameters. Moreover, the decision to take private health insurance instead of statutory health insurance cannot be revised.
There are 118 statutory health insurance providers (by 01-01-2016) in Germany that are in the GKV-Spitzen-verband (statutory health provider union). If you need information on one of them you can use a search function on the website of the union.