I arrived at the bank this morning at the opening time of 8:20, despite which I got into work after 10. Still, having my codice fiscale, passport, work contract, and stub proving I've requested the Permesso di Soggiorno present and correct made the procedure relatively painless.
I have a "conto per non residenti", which means I have to fill in a form every time I pay any money in, but is otherwise the same as a normal account at the Banca CR Firenze (other banks I spoke to wouldn't open a current account for me till I got full residence). It's free till Jan 2007, after which you have to pay banking charges of EUR 6.50 a month in addition to the 8 EUR that the Italian state taxes you for the privilege of having an account every 3 months.
There are some oddities compared to UK system - you can pay in money at any branch of the bank, but you can only withdraw at the branch you opened the account at. (I now ask myself - why did I open the account at the brance nearest my temporary flat rather than, say, the one on Piazza Beccaria next to work? Still, it's only 5 minutes walk). Withdrawal from cash machines costs, even ones of the bank and group. There are so many little banks (they haven't all swallowed each other like in UK) - the group I'm with has banks covering "most of central Italy" and Rome, making travel to, say, Milan no more convenient than travelling abroad. Also, I love the fact that I won't get a Bancomat card till I've had the account for 3 months, instead having to use a 'prepay' card.