Technically speaking, all rental agreeements must be formalized by a legal contract between owner and tenant.
There are a few standard types of contracts, so be sure you have someone you know and trust read through your contract with you before you sign it. Usually the fee for officially registering the contract is divided between owner and tenant.

Special requests
Sometimes landlords will ask the tenant if he/she objects to the landlord registering a lower rental amount than what is actually being paid, in order to save on taxes. A caveat: you will have no way of ever proving that you paid the higher amount should that become an issue, as all of your rent receipts will have a lesser amount than what you actually pay written on them. This system also poses some risk to the landlord, as there are people who decide to accept such terms and then begin paying the lesser written rate. When that happens, there isn't a lot the landlord can  do.

Renting in nero (under the table)
Some landlords avoid paying taxes at all by renting out without a contract. You might decide that this is fine with you. Often the rent is significantly lower than it would be otherwise. Nevertheless, remember that renting without a contract is not legal.

Legal information for tenants
If you have questions about the legality of a contract or about your rights as a tenant in general, contact S.U.N.I.A., a union that represents tenants and renters. Phone numbers for the offices located in neighborhoods around the city may be found in the white pages under the listing S.U.N.I.A, or in the website:
www.sunia.it
SUNIA Bologna
Via Marconi, 49
Tel. 0039 051/268788 - 268700
Fax 0039 051/268811