The codice fiscale is a financial identification number, used in Italy for everything from buying a mobile phone to opening a bank account. If you are planning to live in Rome for any length of time, having a codice fiscale will be vital. Without one, you won't even be able to register a prepay cell phone.
Getting hold of one
The codice fiscale is calculated based on your name and date and place of birth. Fortunately (and unusually for Italy), it's easy to get a codice fiscale. There are even websites where you can punch in your information and get a codice straight back. One of these is Comuni d'Italia.