Travel in Italy does not present any more problems than elsewhere in Europe. Most visitors should be aware of pickpockets and petty thieves, particularly on the trains and metros. Keep all valuables well hidden and ensure all your bags are closed and out of reach of others. Do not accept drinks or food from strangers.
Women travelling alone should be careful as there are reports of sexual harassment.
It is not adviseable to wander around alone at night but if you must the places to particularly avoid would include railway stations, bus stops and deserted piazza's. However there are usually night police patrolling transport areas.
Areas associated with crime tend to also be crowded train stations, on the metros or around tourist locations. Watch your bags and wallets carefully. Southern Italy (eg. Napoli, Sicily, Calabria etc) is generally associated with higher crime so take more care here.
Useful Telephone Numbers if you run into any problems include: Emergency aid services: 113
Police: 112
Fire brigade: 115.
Try to also keep a note of your relevant embassy or consulate in Italy and any other emergency numbers you may require for lost credit cards, travellers cheques.