When to register
Registering your residence in Italy is asked when staying more than 90 days. All citizens (Eu and Non Eu) are advised to register if they are going to stay more than 1 year. 

Please note that tenants have to inform landlord before moving their residence!

When is the permanent registration required?
It is required for several formalities such as registering (on a voluntary basis) with the National Health System (SSN), applying for family reunion (only Non EU citizen), exchanging driving license, enrolling children at school, claiming for family benefit, applying for ISEE certificate, or when applying for the EU long-term residence permit (Non EU citizen only).