Germany has public hospitals, private clinics and charitable hospitals run by church relief organisations; many larger cities have university hospitals as well. As a rule, your general practitioner will arrange to have you admitted to hospital; only in an emergency should you go there directly. Your health insurance will normally cover the costs of your hospital stay. Since hospitalisation can be very expensive, however, it is a good idea to determine in advance whether all of your treatment costs are covered.
National Association of Statutory Health Insurance Funds
Information about the German healthcare system (i.a. German, English, Spanish, French)