Chile is a remarkably safe country. Its violent crime rate is one of the lowest in South America (and much lower than the US). Nevertheless, it still has a healthy nonviolent crime rate. It's a good idea to take precautions, especially against pickpocketing, which is on the rise. Avoid carrying large amounts of money in vulnerable spots. Money belts and leg pouches are two secure means of carrying cash and other important documents.
Santiago's central plazas, Barrio Brasil, markets and bus terminals are prone to pickpockets and petty thievery - as are its buses and metro. Keep an eye on all belongings, and take advantage of the secure left-luggage services at bus terminals and hotels. Violent crime is still fairly unusual in Santiago; men or women can travel in most parts of the city at any time of day or night without excessive apprehension. Valparaíso has a bad reputation for robberies - sometimes violent - in its southern neighborhoods, several of which are best avoided altogether. Beach resorts are prime territory for thievery in the summer, including Viña del Mar, Reñaca and La Serena; avoid leaving valuables on the beach while you go for a swim.
An annoyance rather than a danger are 'students' who hand out poems with a sob story about their financial status and inability to study. They're rarely students, and the poems are rarely theirs. Photographing military installations may lead to getting the film confiscated and possibly a visit to jail.
Chile's stray canine gangs are a growing problem. These are usually not your emaciated, mongrel variety, but well-fed purebreds - especially hoards of German shepherds in the south. In tourist towns, dogs sniff out foreigners and follow them everywhere, but are usually harmless. Unfortunately dog attacks do happen, usually to kids.