Violent crime is relatively rare in Santiago, but petty crime is on the increase and gringos tend to be targets for opportunist thieves. Be on your guard around Plaza de Armas, Mercado Central, Barrio Brasil, Cerro Santa Lucía, and Cerro San Cristóbal in particular. Be careful if you're out on a big night in Bellavista, as organized groups have been known to target drinkers, especially on Pío Nono. You're always safer in a pair or group at night, but Santiago remains one of South America's safest cities - with a little common sense and awareness, the chances of problems are slim.
Around Cerro Santa Lucía and Plaza de Armas someone may hand you poetry on a small slip of paper, telling you how they cannot afford to pay for their studies. They're probably not students and the poems are unlikely to be theirs.