Rome is safe for tourists by any reasonable standard. Pickpocketing is the main concern — it's unfortunately common around the Colosseum, on the 40/64 buses (notoriously tourist-heavy routes to the Vatican), at Termini station, and in crowded sights. Use a money belt or keep valuables in zipped front pockets.
The 'friendship bracelet' scam near the Spanish Steps (someone ties a bracelet on your wrist then demands payment) and fake petitions have been running for decades — simply refuse to stop. Termini station surroundings can feel rough late at night — use taxis or a confident stride. The city is otherwise welcoming and violent crime against tourists is rare.