Towards the end of the Republic, criminals ran wild in Rome. Since there was no police force, there was no one to stop them. It was not safe to walk the streets without a guard. Wealthy Romans hired guards and even built their own small armies to protect their homes and families. This led to further problems when the guards of one wealthy family fought the guards of another family over insults or business territories. The Senate couldn't do anything since there was no money to hire police or even create a militia.
When Rome became an Empire, and emperors were in charge, the emperors used the Roman army to keep order on the streets of Rome.