Foreign students can choose among different options of health insurance.
Please note that for non-EU students it is compulsory to hold a health insurance (or a health insurance payment receipt) in order to apply for the residence permit. The residence permit has the same validity in time of the health insurance.

SSN (Italian National Health Service). Subscription to the SSN it’s not compulsory, however it is warmly suggested because it entitles you to the same treatment as Italian citizens including:
choice of a general practitioner who can visit you free of charge and who will refer you to specialists (dentists, orthopaedics, etc.); free of charge admission to public or certified private hospital;
free of charge doctor on duty-continuous assistance service (guardia medica).

If you already hold a European Health Insurance Card you can access to SSN services without need to subscribe. You may choose instead a general practitioner at the    ASL (Local Health Office)
of your city area.

For details, visit the European Commission site:

http://ec.europa.eu/social/main.jsp?catId=559&langId=en