In an Emergency
To call an ambulance in Italy, dial 118 from your phone.
If you live in a county within the European Economic Area (or Switzerland), you can usually receive free healthcare in Italy as long as you are carrying a valid European Health Insurance Card, or EHIC.
Whether you are covered by the EHIC or will need medical insurance for your trip to Italy, it's best to sort yourself out well in advance. Getting sick in a foreign land without any sort of medical cover can be a stressful and expensive experience.
Europeans and the EHIC
Europeans travelling in Italy are covered under the European health agreements, which means that you shouldn't need to shell out too much money if you get ill. Just make sure you go to a national health doctor (in Italy that's the Servizio Sanitario Nazionale / SSN). It's sensible to confirm any costs before agreeing to treatment.
The EHIC and Brexit
Although the UK has now voted to leave the European Union ("Brexit") at some point in the future, the country is currently still part of the EHIC program. The program includes all members of the European Economic Area, whether EU members or not, including Norway, Iceland, and Liechtenstein, meaning that British residents may continue to be eligible if the UK opts for the so-called 'Norway Model'.
You will however need to carry your European Health Insurance Card, or EHIC. (This is the replacement for the old E111 form, which ceased to be valid back in 2005.) You can apply for an EHIC online at NHS.uk. Do make sure you use the official website to apply for an EHIC: in the past, several scam websites have been set up that charge you to apply, but getting an EHIC through the official website is fast and free.
It's not always necessary to be a citizen to be eligible for the EHIC: for example, if you're based in the UK it's sufficient to be officially resident to get the card.
Many people choose to travel with additional medical cover, granting them access to private medical care. You may, for example, have trouble finding a SSN dentist and some other treatments may not be covered: check with the NHS (or your local European health provider) for more information about any potential limitations of the EHIC.
Americans and other non-Europeans
Visitors from outside Europe are not eligible for the EHIC, and will need to make sure they have adequate medical insurance. American travellers will find more advice on the US Department of State website.