Italy is safe for tourists by any measure. The main concern is pickpocketing, concentrated around tourist sites in Rome (Colosseum, metro), Florence (train station), Naples, and Venice. Use a money belt or keep valuables in front pockets. Be wary of 'friendship bracelet' sellers who tie something on your wrist then demand payment.
Traffic in cities, particularly scooters, can be chaotic — look both ways even on one-way streets. Naples has a reputation that exceeds reality, but standard caution applies. Southern Italy and Sicily are generally safe.