Generally, all students in Germany are obliged to have health insurance until the age of 30. Language - and Ph.D. students are exempt from this rule.
If a person has a state or private health insurance in his or her home country and comes to Germany only for a short period of time, it is possible to be exempt from the health insurance obligation. The consequence of this is however that such a person can never get a state health insurance in Germany in the future.
There are exceptions for students from EU countries and states with which German has a social-insurance-agreement. These students can be exempt from the necessity to get health insurance now but can keep the right to the state health insurance in Germany in the future. For the students from the EU countries it is important to apply for the European Health Insurance Card in their home countries. With this card, it is possible to use the services of a dentist or a hospital in the same way as in the home country and to have it paid by the insurance in the home country. Upon obtaining European Health insurance Card, it is necessary to apply for an exemption confirmation in Germany, for example at AOK.
If somebody is insured only abroad, it is possible that in case of treatment he or she will need to cover the costs first him or herself and only later he or she will get reimbursed by the insurance company.
All students who are in Germany for a period longer than 6 months are advised to get a German health insurance. It is necessary to make sure that medical coverage is sufficient, otherwise in case of illness or accident the patient will need to cover the treatment costs himself.
Term times and tariffs need to be requested from the specific insurance companies. A comparison of insurance for students can be found here.
It is very important to provide your insurance card when visiting a doctor. Otherwise the doctor issues a bill and the patient usually has up to four weeks to pay it. Only then it is possible to apply to the insurance company for reimbursement.