Whether you are covered by the EHIC or need Medical insurance, it's best to sort yourself out in advance.
Europeans
The EHICEuropeans 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).
You will however need your European Health Insurance Card, or EHIC. This is the replacement for the E111 form, which ceased to be valid on 31 December 2005. You can apply for an EHIC over the telephone (call 0845 606 2030 from the UK), at the post office or online.
However, many people choose to get additional medical cover, granting them access to private medical care. You may, for example, have trouble finding a SSN dentist.
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.