No one likes to think about emergencies, but we have to think about them a little in order to prepare for them. (Sorry, friends.)
A few quick and easy things to think about before you leave:
Does your health insurance cover you abroad/if you need to be sent home? Contact them directly and ask.
Bring all of your medicine with you in its original containers.
If you might need a specialist, look for English speaking specialists/clinics ahead of time. Hospitals in major cities should have translators. Read more here about the medical system in Italy.
Register with the U.S. Embassy in Rome for regular security updates.
Leave a copy of your travel plans, passports, credit cards, etc., with a trusted friend at home.
What did I forget?