If you are thinking of coming to Italy, want to open a bank account here, and to use internet banking services, perhaps in connection with doing business in Italy, it is best to avoid the smaller Italian banks.
Online Banking in Italy is Vulnerable to the Mebroot Virus. Indeed, online banking fraud sucked around 3 million Euros from online bank accounts in Italy in 2008. Much of this was down to an insidious little computer virus called Mebroot. This nasty little creature is a dab hand at invisibly installing itself on computers, and back in November 2008, some 24 out of the 35 most commonly used anti-virus programs could not detect Mebroot.
Mebroot sneakily records login information for home banking systems, and then sends it to a third party, who will access said bank accounts and steal money. However, the ability of Mebroot hackers to suck money from home or remote banking systems can be countered.
The Magic Security Key

The bigger banks in Italy provide customers with a little key device which continually generates codes. Before transferring money out of your bank account, you need to enter a code. Mine is a six figure code, incidentally.

Stop reading, start speaking
Stop translating in your head and start speaking Italian for real with the only audio course that prompt you to speak.
As far as I am aware, the Mebroot and other fraudsters have not found a way to circumvent this key based protection system, which means that its users are, for the moment, safe from online banking fraud.
In theory, all Italian banks should provide their customers with such keys. The trouble is that not all do. And more often than not, it is the smaller banks which do not provide their customers with such keys, and are thus render their online banking services vulnerable to internet banking fraud.
Ask for the Security Key
Before opening a bank account in Italy, and especially if you are going to use internet banking facilities, either now or in the near future, ask whether you will be provided with a key, which is a ‘chiavetta elettronica personalizzata‘ in Italian. If the Italian bank does not provide one of these keys, my advice would be to avoid it.
Source: Repubblica online, 27th November, 2008: Nell’internet banking boom del virus-truffa – in Italian.