Stay safe

Like most developed countries, Italy is a very safe country to travel. There are few incidents of terrorism/serious violence and these episodes have been almost exclusively motivated by internal politics. Examples include the 1993 bombing of the Uffizi by the Italian Mafia. Almost every major incident is attributed to organized crime or anarchist movements and rarely, if ever, directed at travelers or foreigners.
Petty crime can be a problem for unwary travelers. Travelers should note that pickpockets often work in pairs or teams, occasionally in conjunction with street vendors. The rate of violent crimes in Italy is considered a "moderate," and while a portion of violent crimes are committed against travelers, it is normally not a problem. However, instances of rape and robbery as a result of drugging are increasing. Travelers should be careful when going out at night alone.
There are many bars in Italy that cater to tourists and foreigners with "home country" themes, calling themselves such things as "American bars" or "Irish pubs". In addition to travelers, these bars attract a large number of Italians who, among other reasons, go there specifically to meet travelers and other foreigners. And while the motivation for the vast majority of these Italians is simply to have a good time with new friends, there can be one or two petty criminals who loiter in and out of these establishments hoping to take advantage of travelers who are disoriented or drunk. Traveling to these places in groups is a simple solution to this problem.
There have been problems in some major Italian cities with police assuming that any Black, East European, or Arab person without an ID card or passport is an illegal immigrant, and treating them accordingly. That could be a considerable problem if you are travelling alone.
For emergencies, call 113 (Polizia), 112 (Carabinieri), 115 (Fire Department) or 118 (Medical Rescue).

Stay healthy

The US Center for Disease Control recommends two vaccines for people traveling to western Europe: Hepatitis A (even though Americans are not at an increased risk) and Hepatitis B.
Italy has a small incidence rate of "Mad Cow" (bovine spongiform encephalopathy (BSE)) disease--about 14 cases per million head of cattle. Since 2001, when Italy had its high of 48 cases of reported BSE, the reports have dropped to 38 (2002), and 29 (2003). Travelers concerned with this should visit the US Center for Disease Control (CDC) website for information on how to limit their exposure.