Considering the volume of tourist traffic, Florence feels remarkably safe and violent crime is rare. However, you need to be on guard against pickpockets in heavily touristed areas, especially the historic centre and Stazione di Santa Maria Novella. Keep only a limited amount of cash on you, and the bulk of your money in replaceable forms such as plastic or travellers cheques. Valuables should be kept in the hotel safe, women should wear their handbag with the strap across their chest, men should carry their swag in their front pockets only and nobody should make themselves a target by wearing an external money belt.
Never leave valuables or anything visible in your car and don't get a hire car that has any markings to identify it as such.
Locals feel completely relaxed about walking around on their own at night, but you should exercise the usual caution: don't go down dodgy-looking alleys or streets and remember there is safety in numbers.