My ranking is based on your chances of getting robbed by a pick pocket or mugger. I’m not counting murders or kidnapping. To construct this list I used personal experience and stories that came back to me from other travelers. It’s by no means scientific, but should give you a good idea of what to expect.
From most dangerous to safest…
Brazil. Everyone seems to get robbed here. All my Brazilian friends have been robbed many many times and I think it was a miracle that I wasn’t, especially during Carnival. This country is not for beginners.
Venezuela. I was there in 2005 but hear it’s since gotten significantly worse. Caracas is the most dangerous city in South America.
Peru. I think there is so much crime here because you have a lot of beginner tourists wanting to see Machu Picchu. Mostly pick pockets and bus theft.
Paraguay. I haven’t heard a lot of stories out of here, and I only spent a week in the capital. It’s on par with Bolivia and Peru.
Bolivia. Outside of La Paz, the danger factor is average. In the medium sized cities I’ve walked around at night without problems.
Colombia. Surprisingly safe if you take basic precautions in cities at night. There are lots of expats here and on average they’ve been mugged “only” once every year or two.
Argentina. Buenos Aires does get a few gringos, but as a whole the country is very safe and I’ve stumbled out of clubs in the middle of the night dozens of times without problems. I don’t know anyone personally who has been robbed in Argentina and I spent almost three months there.
Uruguay. The beach towns are extremely safe. You can leave your belongings for a quick swim and be reasonably certain they’ll be there when you come back. A good beginner trip would be Argentina and then Uruguay.
Chile. It’s very similar to Argentina but I’m giving it the title of safest South American country because I took the Santiago subway with my 40-pound pack to the bus station. Valparaiso has sketchy areas at night but you can tone down the paranoia factor a bit here.
Even though Chile is the “safest” country in South America, keep in mind it’s around two times more dangerous than Washington DC at night. You’ll definitely feel it when the sun comes down. Wherever I am in South America, I fully expect to be robbed every time I walk out the door, so I only take what I need. Worst case I’m out 50 bucks and an old digital camera. My only fear is getting my entire bag robbed. That would be catastrophic.